What is the smallest full square?

What is the smallest full square?

There are many easy calculations in the math. For example, if we say (a) a = (a) 3, then what is the value of a? How to solve it? Very simple. At a glance, it can be said, C = 3. Because the left and right side values ​​of the equation are equal, so the power of A has to be equal. So it can be said C = 3. But there is another solution, which is usually not seen. The second solution is A = 1. Reason (1) 1 = (1) 3

See another simple account. The question is, if the sum of two numbers is 60 and a number is 32 more than the other, then how many numbers are? To find out the answer, we first subtract 32 from 32 and subtract 2 from 2. This will be a small number of values. [(60 - 32) / 2] = (28/2) = 14 So the other number is 32 more. So the other number = (14 + 32) = 46. Their sum = (14 + 46) = 60

This week's puzzle

8, 15 and 20 are the smallest divisions of the total class?

The solution is very simple. Send us your comments in the comments form or at quayum@gmail.com e-mail. See the correct answer online Sunday

Last week's puzzle answers

The puzzle was like this: we know (3) 2 + (4) 2 = 25 = (5) 2. Noticeable, 3 and 4 are two serial numbers. Find out the next two such serial numbers, whose sum is the sum of a whole number?

Answer:

(20) 2 + (21) 2 = (400 + 441) = 841 = (29) 2

The puzzle was quite difficult. But in spite of that, many people gave correct answers. Thank you.

How did you answer?

The easiest way to find out the answers is by checking the sum of the two numbers in the series, whether it is a full-grown or not. It takes a little patience and time.

But there is a formula. I think 'A' is an odd number. Then according to a formula, the sum of the squares of the two ('a' and 'a2') / 2] is equal to the square of [(a2 + 1) / 2]. For example, we can get a = 3, (3) 2 + (4) 2 = 25 = (5) 2. The next section will be in A = 5, (5) 2 + (12) 2 = 169 = (13) 2. But there are 5 and 12 serial numbers, but 12 and 13 are serial numbers. If our problem was such that the sum of the two numbers is the third class of a whole, where the first and second, or the second and the third, the serial number, then this formula can be used effortlessly. In that case, the value of A is 5, 7, 9 or any number of wages, such as 19, we can get respectively

(5) 2 + (12) 2 = (25 + 144) = (169) = (13) 2 (7) 2 + (24) 2 = (49 + 576) = (625) = (25) 2. (9) 2 + (40) 2 = (81 + 1600) = (1681) = (41) 2. Or A = 19 if (19) 2 + (180) 2 = (361 + 324) = (32761) = (181) 2 For each of these numbers, the second and third zodiac signals are serial numbers. For example 5 (12, 13), 7 (24, 25), 9 (40, 41) or 19 (180, 181), etc.

But if the first and second digits are to be two serials, the zodiac sign will be (3) 2 + (4) 2 = (5) 2, (20) 2 + (21) 2 = (29) 2, (119) 2 + (120) 2 = (169) 2, (696) 2 + (697) 2 = (985) 2, (4059) 2 + (4060) 2 = (5741) 2, (2360) 2 + (23661) 2 = (33461) 2 , (137903) 2 + (137904) 2 = (1950255) 2 etc. The first and second ratios are two serial numbers in each of these zodiac signs.

(Grateful: The complicated formulas of the solution are published in the Quraire Digest (5 November 018) Princeton University's Angelos Tsirimokos, BA Mathematics (1974), Queens University, Doug Dillon, PhD, Mathematics, Mathematician Abhinav Sharma) collected from some expert writing).