Question

Find the square root of $0.09$ using Long Division Method

Answer 1

Step 1: Convert decimal to fraction.

We are required to find the square root of $0.09$
Let $$x^2=0.09$$
Converting $0.09$ to fraction, we get

$$\begin{gathered} \Rightarrow x^2=\frac{9}{100} \\ \Rightarrow x=\frac{\sqrt{9}}{\sqrt{100}}...............\left(i\right) \end{gathered}$$

Step 2: Find the square root of the numerator and denominator using the Long Division Method.
Now, we need to find the square root of the numerator $9$.
Applying the long division method, we get,

Step 3: Substitute the values obtained
Now, by substituting these values in the equation $\left(i\right)$ we get
$\Rightarrow x=\frac{\sqrt{9}}{\sqrt{100}}=\frac{3}{10}=0.3$

Hence, the square root of $0.09$ is $0.3$