Question

Evaluate the square root of $60$ in radical form?

Answer 1

Hint: The word radical in the given question means the number should have some type of root in it, it can be a square root or it can be a cube root or even higher roots, for example $\sqrt 3 $ is a radical. The number given in the question has to be solved down to its simplest form possible in terms of a radical. The simplest form for the given number (or radical) will be found out by finding out if any one of the factors of $60$ is a perfect square; the number will come out of the root sign and the remaining number will be the radical form.

Complete step by step solution:
The simplest form for the given number will be found out by finding out if any one of the factors of $60$ is a perfect square the number will come out of the root sign and the remaining number will be the radical form
We now factorize $60$
$60 = 2 \times 2 \times 3 \times 5$
As we can see the number $2$ appears twice. That means the number $4$ which is a factor of $6$ will be a perfect square.
Hence the remaining
$5 \times 3$ will be written in radical form while the number $2$ will be outside as it appears twice.
Thus we write,
$60 = 2\sqrt {15} $
Which is the required answer.
Therefore, the square root of $60$ in radical form is $2\sqrt {15} $.

Note:
If the number does not have any perfect squares as its factor we can say the number is already in its simplest radical form. For example the radical $\sqrt 2 $ does not have any factors which are perfect squares and therefore can be said to be the radical which is already in its simplest form.