Let N be the highest perfect square number less than 124

Find the highest perfect square number less than 124

For n = 1, we have 1^{2} = 1 For n = 2, we have 2^{2} = 4 For n = 3, we have 3^{2} = 9 For n = 4, we have 4^{2} = 16 For n = 5, we have 5^{2} = 25 For n = 6, we have 6^{2} = 36 For n = 7, we have 7^{2} = 49 For n = 8, we have 8^{2} = 64 For n = 9, we have 9^{2} = 81 For n = 10, we have 10^{2} = 100 For n = 11, we have 11^{2} = 121 For n = 12, we have 12^{2} = 144

Since 12^{2} = 144 > 124, we use as our right endpoint. Now, we find the low end number, which is (12 - 1)^{2} = 11^{2} = 121

Therefore, √124 is between 11 and 12

11 < √124 < 12

What is the Answer?

11 < √124 < 12

How does the Estimate Square Roots Calculator work?

Estimates the square root of a number This calculator has 1 input.

What 2 formulas are used for the Estimate Square Roots Calculator?

Take √n

Find n such that (n - 1)^{2} < n^{2} < (n + 1)^{2}