# Can the sum of two perfect squares be a perfect square?

## Can the sum of two perfect squares be a perfect square?

(iii) The sum of two perfect squares is a perfect square.

**What is the formula for the sum of two squares?**

Hence, it is calculated as the total summation of the squares minus the mean….Formulas for Sum of Squares.

Sum of Squares Formulas | |
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In Statistics | Sum of Squares: = Σ(xi + x̄)2 |

For “n” Terms | Sum of Squares Formula for “n” numbers = 12 + 22 + 32 ……. n2 = [n(n + 1)(2n + 1)] / 6 |

### Is the product of 2 perfect squares a perfect square?

The product of two perfect squares is a perfect square.

**Can the sum of two squares equal another square?**

In writing a number as a sum of two squares, it is allowed for one of the squares to be zero, or for both of them to be equal to each other, so all squares and all doubles of squares are included in the numbers that can be represented in this way.

## How do you check if a number is sum of two squares?

1 && x != 0) for (q; (q*q) <= (x/2); q++) if ((x – (q*q)) == (j*j)) printf(“Given number is sum of two squares”); This one sometimes works and sometimes doesn’t, for example it does work for 65 (8^2+1^2) and 90 (9^2+3^2) but wouldn’t work when I put 181 (10^2+9^2) and so on..

**Which numbers can be written as sum of two squares?**

All prime numbers which are sums of two squares, except 2, form this series: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, etc. Not only are these contained in the form 4n + 1, but also, however far the series is continued, we find that every prime number of the form 4n+1 occurs.

### How do you find the number of perfect squares between two numbers?

For example, let b = 24, a = 8. floor(sqrt(b)) = 4, ceil(sqrt(a)) = 3. And number of squares is 4 – 3 + 1 = 2. The two numbers are 9 and 16.

**What is the product of two squares?**

Given a square number n=r2, it is the product of two distinct squares if and only if its square root r can be written as the product of two distinct numbers r=ab.