Question

How do you simplify $\sqrt{192}$?

Answer 1

Hint:The square root of any number is a value that we get when we multiply it by itself and produce the original number.
It’s a simple way to find out the square root of any number, just factories that number and make a perfect square of any number if possible.

Complete step by step solution:
The given square root is $\sqrt{192}$.
Now we factorize the number $192$
$\Rightarrow 192=4\times 4\times 4\times 3$
We can rewrite it as
$\Rightarrow 192=16\times 4\times 3$
Now we will put these all factor $192$ in the square root
$\Rightarrow \sqrt{16\times 4\times 3}$
Here $16$ is the perfect square of $4$ therefore $\sqrt{16}=4$ and
$4$ is also the perfect square of $2$ so, $\sqrt{4}=2$
We rewrite the square root of $\sqrt{192}$ as
$\Rightarrow \sqrt{16\times 4\times 3}=\sqrt{16}\times \sqrt{4}\times \sqrt{3}$
$\Rightarrow 4\times 2\times \sqrt{3}$
$\Rightarrow 8\times \sqrt{3}$
$\Rightarrow 8\sqrt{3}$

Hence the desired simplification form of $\sqrt{192}$ is $8\sqrt{3}$.

Note: There are two things to find out the square root of the number
The first things are that if the number is ending with $1,4,5$ and, $6$ then the number has the perfect square for example $\sqrt{81}=9,\sqrt{64}=8,\sqrt{25}=5$ and, $\sqrt{36}=6$.
And the second thing is that if the number is ending at $2,3,7$ and $8$ then the number will never get the perfect square.