Question

What is the square root of x squared?

Answer 1

Hint: To find the square root of x squared, we have to write it as $\sqrt{{{x}^{2}}}$ . Square root of a number is a value which when multiplied by itself gives the original number. The square root of a squared number removes the square and leaves the number itself with a positive and negative sign.

Complete step by step solution:
We have to find the square root of x squared.
Let us recollect the definition of square root of a number. Square root of a number is a value which when multiplied by itself gives the original number.
Let us suppose that the square root of a number is 25. When we multiply the square root of 25 with itself, we have to get 25, that is, $5\times 5=25$ or $-5\times -5=25$ . Therefore, $\pm 5$ will be the square root of 25.
We usually denote square root as $\sqrt{{}}$ . We usually call this symbol ‘square root’. It can also be called as radical.
Now, let us find the square root of x squared. We can represent this as $\sqrt{{{x}^{2}}}$ .
The square root of a squared number removes the square and leaves the number itself with a positive and negative sign.
$\Rightarrow \sqrt{{{x}^{2}}}=\pm x$ .
Hence, the square root of x squared is $\pm x$.

Note: We can verify whether x is the square root of $\sqrt{{{x}^{2}}}$ . We know that Square root of a number is a value which when multiplied by itself gives the original number. Hence, we can write $x\times x={{x}^{2}}$ . Hence, we have verified the answer.