How do you find a square root to 1 decimal place?

Answer 1

One way to do it would be: multiply your number by 100, then find the nearest 2 perfect squares and interpolate, then divide that number by 10 to get the approximate square root of the original number.

This works because if a = b2, where a is your original number and b would be the square root of that number.

Then multiply both sides by 100 {Note: 100 = 102}

100*a = 100*(b2) = (10²)*b² = (10*b)²

Lets say you want to find the square root of 5, so mult by 100 --> 500

What squares are close to 500? 22² = 484 and 23² = 529

484 is closer to 500 than 529: (529-500=29 & 500-484=16)

So 22² is closer to 500 than 23² & (2.2)² is closer to 5 than (2.3)²

So square root of 5 = 2.2 (to 1 decimal place)

Check your answer: 2.2 * 2.2 = 4.84