Question

What is $\sqrt{12}$ in simplified radical form?

Answer 1

Hint: In this problem we need to find the simplified radical form of the given value. For this we will consider the value which is under the square root. We will write that number in prime factorization form to convert it into exponential form. After getting the exponential form we will apply square root function on both sides of the equation. Now we will simplify the equation by using some basic mathematical operations, exponential formulas to get the required result.

Complete step by step solution:
Given value is $\sqrt{12}$.
Considering the value which is under the square root i.e., $12$.
We can write the number $12$ in prime factorization form as
$12=2\times 2\times 3$
Applying the exponential formula $a\times a\times a\times a\times .....\text{ n times}={{a}^{n}}$ in the above equation, then we will have
$12={{2}^{2}}\times 3$
Applying the square root function on both sides of the above equation, then we will get
$\sqrt{12}=\sqrt{{{2}^{2}}\times 3}$
Using the radical formula $\sqrt{ab}=\sqrt{a}\times \sqrt{b}$ in the above equation, then we will have
$\sqrt{12}=\sqrt{{{2}^{2}}}\times \sqrt{3}$
We know that the functions square root and square are inverse in nature, which means $\sqrt{{{a}^{2}}}=a$. So, we can write the above equation as
$\sqrt{12}=2\sqrt{3}$

Hence the simplified radical form of the given value $\sqrt{12}$ is $2\sqrt{3}$.

Note: In this method we have asked to calculate the simplified radical form only, so we have simplified the value accordingly. In some cases, they may have asked to simplify the value approximately to three digits after decimal, then we need to use the value $\sqrt{3}=1.732$ and simplify the value as $\sqrt{12}=2\left( 1.732 \right)=3.464$.