The square numbers above and below 53 are \(49 = 7^2\) and \(64 = 8^2\). This means that the value of √53 is between 7 and 8, and closer to 7 because 53 is closer to 49 than it is to 64.

For example, suppose you wanted to take the square root of 85. You can observe that ... The ancients loved to estimate numbers. And Hero was into a lot of different things.

Roots are the opposite of powers. As 2 squared is 4, then a square root of 4 must be 2. \(2^2 = 4\). Reversing this gives \(\sqrt{4} = 2\). To find square roots or cube roots, work backwards from ...