One could have guessed two and been right, but this solution is more like a proof demonstrating the use of the quadratic equation, root quattuor, Latin for four because there are four terms, including the zero. I have a friend whose last name is Ekk. If one saw his family approaching, one could say, “Here come the Ekks.” X
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The square root of 9 is 3i. What is i? The answer has to do with complex numbers, not just with the real numbers on the number line. So, i is an imaginary number. For an explanation, see https://www.youtube.com/watch?v=q9wUxUbi1U
Catholic bishops worldwide 5,600
Catholic priests worldwide 416,000 (rounded) 5,600 + 416,000 = 421,600 5,600/421,600 = .01328273 The odds of a Catholic priest becoming a bishop are 5,600 to 421,600. Approximately 1% of Catholic priests will become a bishop. It’s a lopsided chess game right now with small numbers of pawns (priests) trying to hem in Francis, the bad bishop. Alon Amit, PhD in Mathematics and Mathcircler, gives a fantastic answer to the following question: What is the practical usefulness of learning the Nth root of a number? My soontobe 7th grade son asked me: If I/we could think of good reasons for finding 2nd and 3rd root but not the Nth. Any good explanations? Alon relates his math to the piano and a bicycle wheel. Interested? Read the deal … Quora.
https://www.quora.com/WhatisthepracticalusefulnessoflearningtheNthrootofanumber Richard Ferrara, Quora contributor, Software Engineer, Catholic, conservative Republican, Scrabble player, MS Mathematics & Physics, University of Copenhagen (1971), MSc Mathematics, University of Bristol (1990)
What is an uncountable infinity? Let’s say you die and go to Hell. You insist that there has been some mistake and file an appeal with Saint Peter. He convenes a panel of archangels to consider your case. Eventually, a compromise is reached: you can win your soul back, but to do so, you must beat the devil in a guessing game. I. Here’s how it works: the devil writes down a whole number on a piece of paper. This number never changes. It can be any positive whole number — there is no upper limit. It can be 52, a trillion, a googolplex, whatever. [Nineyearold Milton Sirotta coined the term googol, 10 to the 100 power, and then proposed the term googolplex to be “one, followed by writing zeroes until you get tired.”] Each day you get one guess. If you correctly pick the devil’s number, you go free. Otherwise, you’re stuck there for another day. (We assume that you have some foolproof way of keeping track of what numbers you’ve previously chosen, the piece of paper is big enough to fit any number, the devil doesn’t cheat and change it, etc.) What do you do? Well, the bad news is that there’s no telling how long you’ll be in perdition. But the good news is that a simple strategy will get you free. On the first day you guess one. If that’s the devil’s number, great, you’re free. If not, then on the second day you guess 2, then 3, 4, 5, and so on. It may take eons, but eventually you will reach the right number and escape. That’s because even though there are an infinite number of positive integers, it’s a countable infinity — a set whose members can be arranged in order so that you can hit every one of them. The devil cannot pick a number so high or complex that you will never reach it. II. Now let’s change the rules of the game: this time the devil can pick any integer (positive, negative, or zero). Obviously, you can’t follow the same strategy, because you will miss all the negative numbers. However, you can still win. Just start with zero, then plus 1, then minus 1, plus 2, minus 2, and so on. Even though it looks like more choices have been added, the result is still a countable infinity. In math terminology, we say that the cardinality of the set hasn’t changed. (It’s called “alephnull” if you want to get technical.) III. Now let’s change the rules again: this time the devil can pick any rational number (i.e., any number that can be expressed as a fraction). At first glance, it looks like the game is now unwinnable. What’s the fraction with the smallest value greater than zero? One half? No, one third is less. And one fourth is less than that. And what’s the first number greater than one fourth? 2/7? 3/11? You are in trouble now. Or are you? See, there’s a trick: although you need to find some way to order your guesses, you don’t necessarily need to order them by value. A fraction is just a pair of numbers: a numerator and a denominator. Imagine those two numbers as X and Y coordinates on a plane. You can now win the game by starting from the origin and working outward in a spiral. First you guess all the fractions whose numerator and denominator add up to 1. There’s only one of them: 0/1. Next, the ones that add up to 2, which are 0/2 and 1/1. Then 0/3, 1/2, 2/1. And so on. It took some thinking this time, but once again you’ve escaped. IV. Okay, one more: this time the devil can pick any irrational number. It can be pi, or e [Euler’s number, an irrational number with a nonrecurring decimal that stretches to infinity], or the 20th root of a billion, or the square of the cosine of the cube root of the natural logarithm of the hyperbolic tangent of … you get the idea. This time you’re screwed. Going in value order won’t work. Going in a spiral won’t work. Going in alphabetical order by the description of the number won’t work. The number may have an infinitely long description or even none at all. The set of irrationals is an uncountable infinity — there’s no way to order them so that you hit them all. A fellow named Georg Cantor proved it in 1874. Whatever strategy you use, you’re going to miss some numbers. Of course, you could still get lucky. The devil could pick something simple like the square root of 2, and you could just happen to guess it. But you’re no longer guaranteed to win the game. So … enjoy perdition. You’re going to be there for a while. The “period” of a repeating decimal begins immediately after the decimal point. Sometimes, this is referred to as the repeated block.
Write the period of the repeating decimal in the numerator of an ordinary fraction and write some number of nines in the denominator of an ordinary fraction. The number of nines must be equal to the number of digits in the period of the repeating decimal. Take a repeating decimal 0.3 as an example. (A bar over the three is usually used to indicate the three is repeating). It has zero integers and a three in the period, the place after the decimal point. Convert to a fraction. The rule states that the period of a repeating decimal should be written in the numerator of an ordinary fraction. So, in the numerator we write 3. The denominator must contain some number of nines. In this case, the number of nines must be equal to the number of digits in the period of the repeating decimal 0.3. In the repeating decimal the period consists of one three. So, we write one nine in the denominator of the fraction: 3/9 The resulting fraction 3/9 can be reduced by 3, and then we get the following: 1/3 Thus, when one translates the repeating decimal 0.3 into an ordinary fraction, one gets 1/3. Want to try 0.45 repeating? The answer will be 5/11. Quora math question
In my math homework problem, they ask me to prove that a number which is made up with 12 ones and 13 zeros cannot be a perfect square. Can anybody help me prove it? Answered by Sanket Alekar, math & geography nerd turned standup comedian A number with 12 ones and 13 zeros has a sum of 12 when all the digits are added. The number 12 is divisible by three, meaning that the long number is divisible by three. However, 12 is not divisible by nine, meaning that the long number is not divisible by nine. If a number is divisible by three and not by nine, that means it has only one factor of three in its prime factorization. 12/3 = 4, 12 = 3x2x2 (only one 3) As a result, it cannot be a perfect square, because in perfect squares each prime factor must appear an even number of times. E.g.: 3x3 = 9, 2x2x2x2 = 16 [answer edited slightly] I would add, “It is helpful to think of more numbers, such as 27. It does not have an even number of prime factors: 3x3x3. Remember, a prime is divisible only by itself and one. Now, think of 36, a perfect square, which is 2x3x2x3. It has an even number of prime factors, two two’s and two three’s.” Here is an explanation of combinations, the basis of the challenge to Darwin. His Theory of Evolution is challenged by high school math  combinations. Get rid of Darwin. Get rid of Marx. Keep Freud.
I will be reading, Murderous Maths, Do You Feel Lucky? By Kjartan Poskitt, published by Scholastic Children’s Books, London, © 2001, and will write a review in the future. It might have appealed to me when I was reading Mad Magazine, age 12.
Polygon One of the first things children learn about in school is the concept of shapes, and that’s what a polygon is — a figure with at least three straight sides and three angles. Simple polygons include triangles, squares, pentagons, and even stars. However, shapes such as circles, hearts, and moons are not polygons, because they have curves. The word comes from the Greek term polugōnos, meaning “manyangled.” Quadratic equation A quadratic equation involves unknown variables with an exponent no higher than the second power. See the image below. Striking fear into the hearts of many, this equation is important because solving it unlocks a world of mathematical power. The basic formula is used across almost every field of engineering, science, and business. The name comes from the Latin word quadraticus, meaning “made square.” used for solving rectangles
Sir Cumference and the Dragon of Pi, published by Charlesbridge, written by Cindy Neuschwander and illustrated by Wayne Geehan (copyrights 1999), is an excellent math story suitable for elementary school students and adults like me and features a rhyming poem.
Characters: Sir Cumference, father Lady Di of Ameter, mother Radius, son and protagonist Sym, brother Geo of Metry, carpenter Lady Fingers, cousin Lady Fingers helps Radius make the pie. A year ago, or so, a student explained the XBox method to me. We ended up doing the guessing method, which is what I was taught. As far as I can determine, Quora mathematicians use the guessing method. I have seen the XBox used once. I just thought you might like to see the XBox. Though the guessing method is fast, with practice, the XBox works, and now I like it. Even more, I like Mr. Fuller’s advice: do your best and forget the rest. From p 17 –
Quickly, I spotted my first fraud. “That 3/21,” I said. “It’s really a 1/7, isn’t it?” I pointed my Reducer at the fraction and dialed a 3. Both the numerator and the denominator were divided, and now I had a 1/7 before me, as I suspected. Published by Charlesbridge, the book is written by Edward Einhorn, copyright 2014, and illustrated by David Clark, copyright 2014. Fractions are taught early, generally beginning in 3rd grade, but this book is great for all students for its imaginative story and color drawings. I borrowed it and two similar books from Alexander (8). Is there a fast way for squaring numbers that are really big … of more than three digits? Let’s pick this number: 1,002 squared. I chose 1,002 arbitrarily because I like to work with smallish big numbers, but the following formula works for any number.
(a ± b)² = a² ± 2ab + b² a = 1000 (because 1000 is easy to work with) and b = 2 Using the formula, (1000 + 2)² = 1,000,000 + 4,000 + 4 = 1,004,004 When multiplying multiples of 10, just count the zeros. One thousand is a multiple of 10. So, with 1000 x 1000, or 1,000 squared, count the six zeros, and the answer is one million. An odd number can be defined as 2k + 1. What, what? Replace k with any integer, and the result is an odd number. Try 1, then 2, then 3, etcetera. He used FOIL, which is first outer inner last. Need help with math symbols? https://www.mathsisfun.com/sets/symbols.html Can you get a rational number by adding irrational decimals?
Answered by Quora contributor, Manjunath Subramanya Iyer, Math teacher Yes. Two irrational numbers are 2 + √3 5  √3 The square root of three is an irrational number. Adding a number like two or subtracting from five changes nothing. See note below. Their sum (2 + √3) + (5  √3) = 7 Seven is rational. How do we know that? 49/7 = 7 Note: From mathisfun.com – An irrational number is a real number that cannot be made by dividing two integers. Definition of an integer: it has no fractional part. “Irrational” means “no ratio” [Latin comes in handy.], so it isn’t a rational number. Its decimal also goes on forever without repeating. Example: π is an irrational number, as it cannot be made by dividing two integers. Same for √3. Another resource I use for math is mathisfun.com. Here, for example, is an explanation of complex numbers: https://www.mathsisfun.com/numbers/complexnumbers.html
When you hear the phrase, “rational number”, don’t be frightened. Look at the root, rational. [Latin comes in handy.] Thus, a rational number can be written as a ratio, or fraction, which is the same thing: ½. Think of ratio this way: the quantitative relation between two amounts showing the number of times one value contains or is contained within the other. One is a rational number: it can be written as 1/1.
Example: the ratio of dogs to cats is 1 to 2. There is one dog contained in every two cats. Well, in English, we say, “one dog for every two cats”. In Massachusetts, there are 1.6 million cats to 850,000 dogs. The ratio is 1,600,000/850,000, which is 160/85. Just cross out the four zeros on top and the four zeros on the bottom. Use the calculator and the result is in decimal form: 1.88 ferocious felines, almost two, for every friendly Fido. Figures rounded. These numbers are rational numbers. The owners, however, might be irrational. How do I find the square root of 625 without a calculator? New math? I dunno. I try to work with easy numbers, like 200 and 25. Check the answer: 25 X 25 = 625. Where did the 400 come from? I just wanted to reduce the number to something workable. Otherwise, one can do the guessing game, but what if the number is really big?
Density tells how heavy something is, no matter its size. Just by looking at the weight numbers, one can get a better picture of what’s heavier and by how much? Even if a block of iron is the same size as a similarly sized piece of cotton, the iron is denser and, in fact, five times heavier than cotton. Density is the degree of compactness of a substance. I think this applies to bone density. The formula for density ρ when m the mass and V the volume are known is ρ = m/V.
Mass is a measure of the amount of matter in a substance or an object. The basic unit of mass is the kilogram (kg). For an approximate value in pounds, multiply the kg by 2.205. Volume is a measure of how much space an object or substance takes up. The basic unit of volume is the liter (l). For an approximate value in gallons, divide the l by 3.785. I love this number.
Find the sum of all the odd numbers between 10 and 550 that are divisible by three. Answered July 28 by Mike Alexander Studied ALevel Mathematics, Physics & Computer Science So, the odd numbers in the range go: [he shortens lists for visual reasons] 11 13 15 17 19 21 23 25 27 … 543 545 547 549 Every third number in bold is divisible by 3. [Remember the math fact: if the sum of the digits in the number equals three, the number is divisible by three. Try it with each one of the boldface numbers.] So, the sum is 15+21+27+33 … +543+549 Since all terms are divisible by 3, we can write this as: 3(5+7+9+11 … +181+183) [Because multiplication is the inverse of division. Proof: multiply the last number, 183, by three, and the product is 549.] Now notice that the series inside the parentheses is almost a full set of consecutive odd numbers  it just lacks 1+3+ at the start. So, it will be 4 less than the series: I will stop here. If you want the rest of the proof, click https://www.quora.com/HowdoIdothisarithmeticquestionFindthesumofalltheoddnumbersbetween10and550thataredivisibleby3 The final answer is 25,380. Guess what? The answer is divisible by three. How do I quickly convert eightfifths into a decimal?
8/5 = 1 + 3/5 1 + 3/5 = 1 + 6/10 6/10 = .6 add .6 back to 1 8/5 = 1.6 3 Not all numbers ending with nine are divisible by three such that the quotient (result) is a whole number. Twodigit numbers ending with nine and not divisible by three are 19, 29, 49, 59, 79, 89, and so on, and threedigit numbers not divisible by three are 109, 199, and so on. However, if the sum of all the digits in the number is divisible by three, the number is divisible by three. For example, if the number is 657, the number is divisible by three: 6 + 5 + 7 = 18, which is divisible by three. Three makes me think, Trinity. Update: Alexander (8) learned this math fact today, 8/4/2022. 
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