Question

How do you simplify ${x^4}$?

Answer 1

Hint:
Here we need to find the root of the number ${x^4}$ and for this we must know that whenever we need to take the root, we need to actually find the number which when multiplied by itself gives the number whose square root is to be taken. We can also write the number inside the root in the form of its factors and then we can take the number out of the pair outside the root.

Complete step by step solution:
Here we are given to find the root of the number that is given as ${x^4}$.
For this, we must know what actually square root means. The square root of any number that says $a$ is denoted by the symbol which is represented as $\sqrt a $ and for this we actually need to find the number which when multiplied by itself gives the number inside the root. The example will make it clearer.
For example: If we need to find the square root of the number $9$ then we can see that $3 \times 3 = 9$ which means that when $3$ is multiplied by itself gives the number $9$ so we can say that $\sqrt 9 = \pm 3$
Here we need to use both the signs of as $\left( { - 3 \times - 3} \right) = 9$
Hence we will write the answer as $\sqrt 9 = \pm 3$
Now similarly we can write ${x^4}$ as $x \times x \times x \times x$
Then we will get:
$\sqrt {{x^4}} = \sqrt {\left( x \right)\left( x \right)\left( x \right)\left( x \right)} $
As there are $2$ pairs of $x$ that are multiplied so we can take two $x$ outside the root and we can write the square root as:

$\sqrt {{x^4}} = \sqrt {\left( x \right)\left( x \right)\left( x \right)\left( x \right)} $$ = \pm \left( x \right)\left( x \right) = \pm {x^2}$.

Note:
Here the student must know the difference between the terms square root and the square of any number. The square root of any number means to find the number which when multiplied by itself gives the number inside the root and the square of the number means to multiply it by itself and write the result.