Question

What are the positive and negative square roots of $36$?

Answer 1

Hint: From the question given we have to find the positive and negative square root of $36$. As we know that the all-positive real numbers have a positive and negative real square root which are additive inverses of one another. The principal square root is the positive one and is the mean when we use the symbol $\sqrt{{}}$. If we want to refer to the negative square root, then just put a minus sign in front of the symbol that is $-\sqrt{{}}$.

Complete step by step solution:
From the given question we have to find the positive and negative square root of
$\Rightarrow 36$
Both $6$ and $-6$ are square roots of $36$ since they both $36$ when squared, that is,
$\Rightarrow {{6}^{2}}=6\times 6=36$
$\Rightarrow {{\left( -6 \right)}^{2}}=-6\times -6=36$
As we know that the all-positive real numbers have a positive and negative real square root which are additive inverses of one another.
The principal square root is the positive one and is the mean when we use the symbol $\sqrt{{}}$.
By this we will get,
$\Rightarrow \sqrt{36}=6$
If we want to refer to the negative square root, then just put a minus sign in front of the symbol that is $-\sqrt{{}}$.
By this we will get,
$\Rightarrow -\sqrt{36}=-6$

Therefore, the positive and negative square roots of $36$ are $6$ and $-6$

Note: students should read the question very carefully, for suppose if student understood the negative square root of $36$ as $ \sqrt{-36}$ instead of $-\sqrt{36}$ then the answer we get will be in complex number, The whole answer will be wrong.