Question

Find the square root of $324$ by the method of repeated subtraction.

Answer 1

Compute the required square root:

We subtract successive odd numbers starting from $1$ as:

$$\begin{gathered} 324-1=323 \\ 323-3=320 \\ 320-5=315 \\ 315-7=308 \\ 308-9=299 \\ 299-11=288 \\ 288-13=275 \\ 275-15=260 \\ 260-17=243 \\ 243-19=224 \\ 224-21=203 \\ 203-23=180 \\ 180-25=155 \\ 155-27=128 \\ 128-29=99 \\ 99-31=68 \\ 68-33=35 \\ 35-35=0 \end{gathered}$$

We observed that, $324$ reduces to $0$ after subtracting $18$ odd numbers.

Hence, the square root of $324$ is $18$.