Question

What is the square root of ${{\left( -12 \right)}^{2}}$ ?

Answer 1

Hint: We need to find the square root of ${{\left( -12 \right)}^{2}}$. We start to solve the given question by finding out the value of ${{\left( -12 \right)}^{2}}$. Then, we find the square root of the simplified expression to get the desired result.

Complete step-by-step answer:
We are given an expression and need to find out the square root of ${{\left( -12 \right)}^{2}}$ . We will be solving the given question by finding out the value of ${{\left( -12 \right)}^{2}}$ and then finding out the value of the square root of the given expression.
The square of a number is defined as the result of multiplying the number by itself. The square of a number $n$ is given by $n\times n$ also written as ${{n}^{2}}$ .
Let us now understand how to evaluate the square of a number through an example.
Example:
What is ${{5}^{2}}$?
The square of the number 5 is obtained by multiplying the number 5 with itself.
Applying the same, we get,
$\Rightarrow 5\times 5$
The product of number with itself that is $n\times n$ can be also written as ${{n}^{2}}$ .
Writing the same, we get,
$\Rightarrow {{5}^{2}}$
The result of the above expression is $25\;$
Substituting the same, we get,
$\therefore {{5}^{2}}=25$
According to the question, we need to find the value of ${{\left( -12 \right)}^{2}}$
$\Rightarrow {{\left( -12 \right)}^{2}}$
Expanding the square, we get,
$\Rightarrow {{\left( -12 \right)}^{2}}=-12\times -12$
From the rules of arithmetic, we know that $\left( - \right)\times \left( - \right)=\left( + \right)$
Applying the same, we get,
$\therefore {{\left( -12 \right)}^{2}}=144$
Now, we need to find the value of the square root of ${{\left( -12 \right)}^{2}}$
Applying square root on both sides for the above equation, we get,
$\Rightarrow \sqrt{{{\left( -12 \right)}^{2}}}=\sqrt{144}$
The square root of 144 is equal to $\pm 12$
Substituting the same, we get,
$\therefore \sqrt{{{\left( -12 \right)}^{2}}}=\pm 12$

Note: We should remember that the square root of $\sqrt{144}$ is equal to $-12\text{ and }+12$ and not only $+12$ because the number 144 can be represented as follows,
$\Rightarrow 144=12\times 12$
$\Rightarrow 144=\left( -12 \right)\times \left( -12 \right)$
So, the square root of the number 144 can be positive or negative and hence represented as $\pm 12$