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

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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].

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].

Last updated date: 25th Sep 2023

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