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

Last updated date: 17th Jun 2024
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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.

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.