Question

Find the square root of $100$ and $169$ by the method of repeated subtraction.

Answer 1

(i) $100-1=99$
$99-3=96$
$96-5=91$
$91-7=84$
$84-9=75$
$75-11=64$
$64-13=51$
$51-15=36$
$36-17=19$
$19-19=0$
We get $0$ in the ${10}^{th}$ step.

So, $\sqrt{100}=10$

(ii) $169-1=168$
$168-3=165$
$165-5=160$
$160-7=153$
$153-9=144$
$144-11=133$
$133-13=120$
$120-15=105$
$105-17=88$
$88-19=69$
$69-21=48$
$48-23=25$
$25-25=0$
We get $0$ in ${13}^{th}$ step.

So, $\sqrt{169}=13$.