Question

How do you simplify $ \sqrt{\dfrac{72}{3}} $ ?

Answer 1

Hint: To simplify a given square root we need to factorize a number. Then we will simplify the given expression by finding the square root of 72 and 3. Substituting the values obtained in the given expression gives the simplest radical form.
We have been given an expression $ \sqrt{\dfrac{72}{3}} $ .
We have to simplify the given expression.
We can rewrite the given expression as
 $ \Rightarrow \dfrac{\sqrt{72}}{\sqrt{3}} $

Complete step by step answer:
We know that a number of the form $ \sqrt{x} $ is a real number, where $ x $ is called the radicand and the symbol $ \sqrt{{}} $ is known as radical symbol. The word radical in mathematics denotes the root or square root. Every number has two roots either positive or negative.
Now, we have to solve the obtained expression. We need to calculate the square root of 72 and the square root of 3. We know that when a number is multiplied by itself it is known as the square of that number.
We know that 72 is not a perfect squares so we can factorize as
\[\Rightarrow 72=2\times 2\times 2\times 3\times 3\]
Now, we can write as
 \[\begin{align}
  & \Rightarrow 72=2\times 3\sqrt{2} \\
 & \Rightarrow 72=6\sqrt{2} \\
\end{align}\]
Now, substituting the values we get
 $ \Rightarrow \dfrac{\sqrt{72}}{\sqrt{3}}=\dfrac{6\sqrt{2}}{\sqrt{3}} $
Now, we get the simplest form as $ \Rightarrow \dfrac{6\sqrt{2}}{\sqrt{3}} $ .

Note:
If the given number is a perfect square we can directly write the square root of that number. A perfect square is a number that is expressed as a product of two equal integers. For example, 9 is the perfect square because we can write it as $ 9=3\times 3. $ Here in this question for simplifying further students can substitute the values of $ \sqrt{2} $ and $ \sqrt{3} $ in the obtained expression.