Question

Help is very much appreciated!!! I have no idea if it's true for all values or not.​

Answer 1

It's only valid when the product of m and n is zero, that is when n=0 or m=0

Explanation:

Square roots

Taking the square root of a real number m (non-negative) means to find another number x, such that

`m=x^2`

When we find square roots in algebraic expressions and we need to get rid of them, we take the 2nd power of the roots to eliminate them

We have to test if

`√(m+n)=√(m)+√(n)`

for all values of m and n

To find an answer, we take the second power in both sides:

`\left ( √(m+n) \right )^2=\left ( √(m)+√(n) \right )^2`

Expanding

`m+n=m+2√(mn)+n`

Simplifying

`2√(mn)=0`

Operating

`mn=0`

The original expression is only valid when the product of m and n is zero, that is when n=0 or m=0