Question

How do you simplify \[\sqrt {{x^5}} \] ?

Answer 1

Hint: For simplification of such terms you need to write the equation in the simplest possible form, that is the root sign should be removed and the power of root need to be attach with the already power of the variable, this all can be done by removing the root sign and putting the value of root.

Complete step-by-step answer:
Now removing the root and then substituting the power of the root in the given question we get;
 \[ \Rightarrow \sqrt {{x^5}} = {\left( {{x^5}} \right)^{\dfrac{1}{2}}}\]
Now according to the algebraic identity, which shows the formula for power solving for any given variable, the algebraic identity is;
 \[ \Rightarrow {\left( {{a^m}} \right)^n} = {a^{m \times n}}\]
We get;
 \[ \Rightarrow {\left( {{x^5}} \right)^{\dfrac{1}{2}}} = {x^{5 \times \dfrac{1}{2}}} ={x^{\dfrac{5}{2}}}\]
This is the required simplest form of the given equation.
So, the correct answer is “${x^{\dfrac{5}{2}}}$”.

Note: In the given question you can also try to add and minus any number inside the root to make a perfect square but that will work here as no other term with “x” is given in the question, hence no need for such kind of expansion is needed here.
The best possible way to solve this question is this only, if you want to check then you can go in the reverse direction and just put the root again removing the half power from the variable and you will get your equation again. But some rearrangement is possible here like removing the “x- square” term outside of the root then solving the question, but with that also the same result will be obtained.