Question

What is the square root of $\dfrac{27}{9}$ ?

Answer 1

Hint: We need to find the square root of the fraction $\dfrac{27}{9}$ . We start to solve the given question by finding out the value of the fraction $\dfrac{27}{9}$ . Then, we find the square root of the simplified expression to get the desired result.

Complete step by step solution:
We are given an expression and need to find out the square root of $\dfrac{27}{9}$ . We will be solving the given question by finding out the value of $\dfrac{27}{9}$ and then finding out the value of the square root of the given expression.
According to the question, we need to find the value of $\dfrac{27}{9}$
$\Rightarrow \dfrac{27}{9}$
Writing the numerator and denominator as the product of prime factors, we get,
$\Rightarrow \dfrac{3\times 3\times 3}{3\times 3}$
Canceling the common factors, we get,
$\Rightarrow 3$
Now, we need to find the value of the square root of the number $3$
Applying square root for the number 3 in the above expression, we get,
$\Rightarrow \sqrt{3}$
The square root of the number 3 is equal to $\sqrt{3}$
Substituting the same, we get,
$\therefore \sqrt{\dfrac{27}{9}}=\sqrt{3}$

Note: The result for the given question can be cross-checked using the equation $\sqrt{\dfrac{27}{9}}=\sqrt{3}$ as follows,
LHS:
$\Rightarrow \sqrt{\dfrac{27}{9}}$
We know that the number 27 can be expressed as the product of prime factors as follows,
$\Rightarrow 27=3\times 3\times 3$
 Following the same, the number 9 can be expressed as the product of prime factors as follows,
$\Rightarrow 9=3\times 3$
Substituting the values of the numbers 27 and 9 in the above expression, we get,
$\Rightarrow \sqrt{\dfrac{3\times 3\times 3}{3\times 3}}$
Canceling out the common factors, we get,
$\Rightarrow \sqrt{3}$
RHS:
$\Rightarrow \sqrt{3}$
LHS = RHS. The result obtained is correct.