Question

Find the square root of $44$ in simplified radical form.

Answer 1

Hint: In the given question, we are required to find the square root value of the number $44$ in simplified radical form. Square root of a number is a value, which when multiplied by itself gives the original number. Here we can see that $44$ is not a perfect square. Now, to simplify the square root of $44$, we first do the prime factorization of the number and take the factors occurring in pairs outside of the square root radical.

Complete answer:
Given, $44$
$44$ can be factorized as,
$44 = 2 \times 2 \times 11$
Now, expressing the prime factorization in powers and exponents, we get,
$44 = {2^2} \times 11$
We can see that $2$ is multiplied two times and hence the power of $2$ is two.
Now, $\sqrt {44} = \sqrt {{2^2} \times 11} $
Now, we know that ${2^2}$ is a perfect square. So, we can take this outside of the square root we have,
So, $\sqrt {44} = 2 \times \sqrt {11} $
Since $11$ is not a perfect square, we can multiply this and keep it inside the square root. Hence, we get,
$ \Rightarrow \sqrt {44} = 2\sqrt {11} $
This is the simplified radical form of the square root of $44$ as required in the problem.

Note:
We do the prime factorization of the number whose square root is to be found so as to find the constituent prime factors of a number in pairs of two. We take out the factors that occur in pairs out of the square root radical to simplify the expression. Here $\sqrt {} $ is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand.