Question

Question 133

Solve the following question:

Find the square root of 324 by the method of repeated subtraction.

Answer 1

Given number is 324
Now, we subtract successive odd numbers starting from 1 as follows:
Here, 324 - 1 = 323, 323 - 3 = 320
320 - 5 = 315, 315 - 7 = 308
308 - 9 = 299, 299 - 11 = 288
288 - 13 = 275, 275 - 15 = 260
260 - 17 = 243, 243 - 19 = 224
224 - 21 = 203, 203 - 23 = 180
180 - 25 = 155, 155 - 27 = 128
128 - 29 = 99, 99 - 31 = 68
68 - 33 = 35, 35 - 35 = 0

We observe that the number 324 reduced to zero (0) after subtracting 18 odd numbers.
So, 324 is a perfect square of 18.
$\therefore \sqrt{324}=18$
Hence, the square root of 324 is 18.