Question

What is the square root of 37 in the simplest radical form?

Answer 1

Hint: To write the square root of 37 in the simplest radical form we are going to write prime factorization of 37 and then we will arrange the factorization in such a way so that we will get some even powers of the factors. And then we can put those factors outside the square root symbol.

Complete step-by-step solution:
In the above problem, we are asked to write the square root of 37 in the simplest radical form so we are going to first of all write 37 in square root form as follows:
$\sqrt{37}$
Now, we are going to factorize the number 37. As 37 is a prime number so only two factors are possible for this number 37, one of the factors is 1 and the other factor is 37. So, writing the factors for 37 we get,
$37=1\times 37$
Now, substituting the above factor form in place of 37 in $\sqrt{37}$ we get,
$\sqrt{1\times 37}$
In the above square root expression, we cannot take any of the two numbers 1 and 37 outside the square root because both of the two numbers don’t have any power which is even.
Hence, the square root of the simplest radical form of 37 is $\sqrt{37}$.

Note: You can also find the square root of 37 in simplest radical form by writing 37 in the form of the square of highest number multiplied with some other number. For e.g. if we have say 72 and we have to find the square root of 72 then the highest square of a number which on multiplication with some number will give 72.
The highest square of a number which can be possible is 36 which is the square of 6 and on multiplying 36 by 2 we will get 72 and we can write 72 as:
$72=36\times 2$
Now, writing 72 in the square root in the above form we get,
$\sqrt{72}=\sqrt{36\times 2}$
As 36 is the square of 6 so we can take 6 out from this square root and we get,
$\sqrt{72}=6\sqrt{2}$
In this way, you can do for the square root of 37 also.