Question

How do you simplify $\sqrt{128}$ ?

Answer 1

Hint:
For finding the square root of $128$ we need to break down this number into the product of numbers by doing the prime factor. Then we will solve this by making a pair if it will be otherwise we will write the same as we got from the factor.

Complete Step by Step Solution:
So the prime breakdown of the number $128$ will be
$\Rightarrow 128=2\times 64$
Again doing the breakdown of $64$ , we will get
$\Rightarrow 128=2\times 2\times 2\times 16$
Again doing the breakdown of $16$ , we will get
$\Rightarrow 128=2\times 2\times 2\times 2\times 8$
Similarly, we will do this breakdown till possible and finally, we will get the number
$\Rightarrow 128=2^7$
So, now from the question, we can write it as
$\Rightarrow \sqrt{128}=\sqrt{2^7}$
The right side of the equation can be written as
$\Rightarrow \sqrt{128}=\sqrt{2^6\times 2^2}$
Again the right side of the equation can be written as
$\Rightarrow \sqrt{128}=2^3\sqrt{2}$
And on solving the above equation, we get
$\Rightarrow \sqrt{128}=8\sqrt{2}$

And therefore, the square root of $128$ will be $8\sqrt{2}$.

Note:
This can be solved by using the shorter way too. Only we need to break it into such a way that there should be a square of it. Like we can write the above question as
$\Rightarrow \sqrt{128}=\sqrt{64\times 2}$
And taking the RHS, we will split both the root so we get
$\Rightarrow \sqrt{128}=\sqrt{64}\times \sqrt{2}$
And as we know that $\sqrt{64}=8$ , hence by substituting this value, we will get the equation as
$\Rightarrow \sqrt{128}=8\sqrt{2}$
So, in this way also we can solve such types of questions.