Question

Find square root of $4489$ using repeated subtraction.

Answer 1

Square root of 4489 using repeated

Subtraction

The squarer any natural number n can

be ax pressed as the sum of n consecutive

odd numbers

This is when for finding the square

root of $4489$ we need to keep

subtracting odd natural consecutive

numbers until we get a zero

This processed as follows

Step $1:4489-1=4488$

Step $2:4488-3=4485$

Step $3:4485-5=4480$

By subtracting consecutive odd numbers

in the same manner we get

Step $67:133-133=0$

$\Rightarrow 4489$ is obtained by adding 67

consecutive odd numbers

$\therefore$ Square root of $4485$ is $67$