Question

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

Answer 1

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].