Question

Find the square roots of $100and169$ by method of repeated substraction.

• A. $10;13$
• B. $10;17$
• C. $20;13$
• D. $20;17$

Answer 1

The correct option is A $10;13$

For $\sqrt{100}$
$100-1=99$
$99-3=96$
$96-5=91$
$91-7=84$
$84-9=75$
$75-11=64$
$64-13=51$
$51-15=36$
$36-17=29$
$19-19=0$

For $\sqrt{169}$
$169-1=168$
$168-3=165$
$165-5=160$
$160-7=153$
$153-9=144$
$144-11=133$
$133-13=120$
$120-15=105$
$105-17=88$
$88-19=69$
$69-21=48$
$48-23=25$
$25-25=0$

From $100and169$ we have substracted successive odd numbers starting from $1$ and obtained $0$ at $10thand13th$ steps, respectively.
So, $\sqrt{100}=10and\sqrt{169}=13$.