Question

# Find the square root of $125$ using repeated subtraction.

Verified
159k+ views
Hint- Keep subtracting the odd numbers starting from $1$ till we get $0$. As it is given in the question that uses repeated subtraction under this we will subtract odd numbers starting from $1$ till the point we get $0$. If $125$ is a perfect square then Repeated subtraction will give $0$.
Step$1$, we will subtract odd number $1$ i.e.
$125 - 1 = 124$
Step$2$, we will subtract odd number $3$ i.e.
$124 - 3 = 121$
Same steps will be repeated until we get zero or negative values.
Step$3$. $121 - 5 = 116$
Step$4$. $116 - 7 = 109$
Step$5$. $109 - 9 = 100$
Step$6$. $100 - 11 = 89$
Step$7$. $89 - 13 = 76$
Step$8$. $76 - 15 = 61$
Step$9$. $61 - 17 = 44$
Step$10$. $44 - 19 = 25$
Step$11$. $25 - 21 = 4$
Step$12$. $4 - 23 = - 21$
Since by repeated subtraction, we do not get the answer as zero at any point, $125$ is not a perfect square.

Note- In this type of question if the number is perfect square then repeated or successive subtraction will give zero value in the end [as in our case $125$ is not a perfect square therefore at ${12^{th}}$ step we got negative value].