Question

Describe how you would estimate the square root of a number that is not a perfect square without using a calculator.

Answer 1

The square root must be between the square roots of the perfect squares just above and just below your number. 

For example the square root of 89 must be between 9 and 10.

Answer 2

Answer:

We will take a number say 105. To find its square root, proceed as under:

• Find the closest perfect square to it. Here, it is 100.

• Find square root of that number, i.e. 100. We know the square root is 10.

• Divide the number by the square root calculated above. Here, 105÷10.

• Take the mean of the result obtained above and the square root in step 2. Here, (10+10.5)/2 = 10.25

The number obtained above is the square root of the required number.

Also we can consider second example as:

We have to find square root of 420.

• Closest perfect square is 400.

• Square root of 400 is 20.

• 420÷20 is 21.

• Mean of 20 and 21 is 20.5

• Square root of 420 is 20.5