Question

Express 31 square as a sum of four perfect squares

Answer 1

Answer:

What Is the Sum of Perfect Squares Formula?

The formula for finding the sum of two perfect squares is derived from one of the algebraic identities, (a + b)2 = a2 + 2ab + b2, which is: a2 + b2 = (a + b)2 - 2ab.

The formula for finding the sum of the squares for first "n" natural numbers is: 12 + 22 + 32 + ...

Answer 2

Answer:

Concept:

A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, $9$ is a square number since it equals $3^{2}$ and is represented by the symbol $3\times 3$.

Step-by-step explanation:

Given:

Express 31 square as a sum of four perfect squares

To find:

Sum of four perfect squares that results in square of $31$

Solution:

Theorems relating to the expression of integers as sums of squares of other integers are known as sum of squares theorems in additive number theory.

• Square of $31$ is $31^{2} =31 \times 31$

              $31^{2} =961$

• Find squares of four numbers that produces $961$ as result.

                              $961=841+100+16+4$

                               $31^{2} =29^{2} +10^{2} +4^{2} +2^{2}$

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