Question

How do you simplify $\sqrt {60} $ ?

Answer 1

Hint:
Since we know that $60$ is not a perfect square, the value we will get will still include a radical. So we will solve it by taking the factors of $60$. And solving it, we will get the solutions. So the only condition for it is, we can solve any square root if the number has any factors.

Complete Step by Step Solution:
Here in this question we have to simplify $\sqrt {60} $ and for this, we will first find the factors of it.
The factors of $60$ will be equal to $2 \times 2 \times 5 \times 3$
So, mathematically it can be written as
$ \Rightarrow \sqrt {60} = \sqrt {2 \times 2 \times 5 \times 3} $
Now on rewriting the above equation in the manner of exponential, we will get the equation as
$ \Rightarrow \sqrt {60} = \sqrt {{2^2} \times 5 \times 3} $
Since, the exponential components and the root will cancel out each other, so on solving it again we can write the equation as
$ \Rightarrow \sqrt {60} = 2\sqrt {5 \times 3} $
And on solving the multiplication which under the root, we will get the expression as
$ \Rightarrow \sqrt {60} = 2\sqrt {15} $

Hence, on simplifying $\sqrt {60} $, we get $2\sqrt {15} $.

Note:
There is also another way of solving this question. So for this, we just have to find the LCM of the number. So on taking the LCM of $60$ , we will get $2 \times 2 \times 5 \times 3$.
Now the number which is repeated two, four, and six. That is only even for the even root will be considered and will be in front of the root. And in this way of solving it, we will get $2\sqrt {15} $ . So we had seen both the procedures for simplifying it. It depends on us which way we are taking.