Question

What is the square root of $21$?

Answer 1

Find a square root using prime factorization method:

The prime factorization method involves expressing numbers as a function of their prime factors.

Apply the prime factorization method.

The prime factorization of $21$ is $7\times 3$

$$\begin{gathered} \Rightarrow \sqrt{21}=\sqrt{(7\times 3)} \\ \Rightarrow \sqrt{21}=\sqrt{7}\times \sqrt{3} \end{gathered}$$

Write the value of the square roots :

$\sqrt{7}=2.646$ and $\sqrt{3}=1.732$

Substitute the values of $\sqrt{7}$ and $\sqrt{3}$:

$$\begin{gathered} \sqrt{21}=2.646\times 1.372 \\ \Rightarrow \sqrt{21}=4.582 \end{gathered}$$

The square root of $21$ is equal to $4.582$.