Question

How do you simplify $\sqrt {{y^6}} $ ?

Answer 1

Hint: Simplification is the process of reducing a fraction to its lowest and simplest possible term or value by cancelling to the lowest common factor of both the numerator and the denominator.

Complete step by step answer:
By the use of simplification we can make an algebraic expression easily understandable and solvable. There are two methods of Simplification. The first method is the use of prime factorization and then dividing the both numerator and denominator by their common factor. While the second method is dividing the common factor without completing the prime factorization of each term.

Process of Simplification of an algebraic expression step by step:-
- First we should write down the factors of both the numerator and the denominator.
- After that we should determine the largest factor which is generally common to both.
- Then we will divide the numerator and denominator by their greatest common factor which is generally known as HCF.
- The final step is to write down the reduced fraction.

Now we will simplify the given question that is to simplify $\sqrt {{y^6}} $
As we know that we can write the square root in terms of fraction as half power $\dfrac{1}{2}$.
Thus, by using this concept we can write $\sqrt {{y^6}} $ as ${\left( {{y^6}} \right)^{\dfrac{1}{2}}}$.
$ = {\left( y \right)^{6 \times \dfrac{1}{2}}}$
$ = {y^3}$
Thus, ${y^3}$ is the simplification of $\sqrt {{y^6}} $

Note: Simplification has made our life very easier, as it helps in reducing a fraction. It can simplify an expression in its most efficient and compact form without affecting its value.