Question

How do you simplify: square root of $\dfrac{1}{16}$?

Answer 1

Hint: Here in this question we have to find the square root of the given fraction. First we will apply the square root to the given number. Then we find the square root of 16 by writing the factors and then by taking the common multiples we get the desired answer.

Complete step by step solution:
We have been given an expression square root of $\dfrac{1}{16}$.
We have to simplify the given expression.
Now we can write the given expression as $\sqrt{\dfrac{1}{16}}$
Now, we know that the square root is applicable on both numerator and denominator. Also we can separately write the numbers with square roots. Then we will get
$\Rightarrow \dfrac{\sqrt{1}}{\sqrt{16}}$
Now, we can write the 16 in factors form as
$\Rightarrow 16=4\times 4$
Also we know that when 1 multiplied by itself it gives the result 1. So the square root of 1 is also 1.
Now, substituting the value we will get
\[\Rightarrow \dfrac{1}{\sqrt{4\times 4}}\]
Now, a number is multiplied twice so write it in an exponential form we will get
\[\Rightarrow \dfrac{1}{\sqrt{{{4}^{2}}}}\]
Now, square and square root cancel each other so we will get
\[\Rightarrow \dfrac{1}{4}\]
Hence by simplifying the given expression square root of $\dfrac{1}{16}$ we get the value as \[\dfrac{1}{4}\].

Note:
Here the given number is a perfect square, so directly obtain the square root. If the number is not a perfect square then we can factorize the number and write the number in the form of exponential and then simplify the number.