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How do you put $ \sqrt{\dfrac{4}{49}} $ in simplest radical form?

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Last updated date: 17th Jun 2024
Total views: 385.2k
Views today: 5.85k
Answer
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Hint: To write the simplest radical form of a square root we need to factorize a number. Then we will simplify the given expression by finding the square root of 4 and 7. Substituting the values obtained in the given expression gives the simplest radical form.

Complete step by step answer:
We have been given an expression $ \sqrt{\dfrac{4}{49}} $ .
We have to find the simplest radical form.
Now, we know that radical means square root.
We can rewrite the given expression as
 $ \Rightarrow \dfrac{\sqrt{4}}{\sqrt{49}} $
Now, we have to solve the obtained expression. We need to calculate the square root of 4 and the square root of 49. We know that when a number is multiplied by itself it is known as the square of that number.
We know that 4 and 49 both are perfect squares so we can factorize both as
 $ \begin{align}
  & \Rightarrow 4=2\times 2 \\
 & \Rightarrow 49=7\times 7 \\
\end{align} $
So we get the values
\[\begin{align}
  & \Rightarrow \sqrt{4}=2 \\
 & \Rightarrow \sqrt{49}=7 \\
\end{align}\]
Now, substituting the values we get
 $ \Rightarrow \dfrac{\sqrt{4}}{\sqrt{49}}=\dfrac{2}{7} $
Now, we get the simplest form as $ \dfrac{2}{7} $ .

Note:
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.