Square Root of 500 Squared (√500^2)

Square Root of 500 Squared

Here we will discuss and calculate the square root of 500 squared. The problem in mathematical terms that we want to solve is displayed below:

√500²

We are doing two math operations: The radical sign √ means that you are taking the square root of 500 and the ² means to square 500. It does not matter which order you do the math operations in, because the following two math rules result in the same answer:

√x² = x

(√x)² = x

Based on those two rules, you can conclude that the answer to our problem is 500. Nevertheless, read on because we will show you different ways of calculating the square root of 500 squared to prove that the answer is 500.

We start by first taking the square root of 500 and then square that result to get our answer like this:

√500 = 22.3607

22.3607² = 500

Now, we will do the operations in opposite order where we first square 500 and then calculate the square root of the result:

500² = 250000

√250000 = 500

You may also find this math rule interesting when dealing with a problem like the square root of 500 squared:

√x² = √x · √x

It also proves that the square root of 500 squared equals 500.

√500² = √500 · √500

√500 · √500 = 22.3607 · 22.3607

22.3607 · 22.3607 = 500

Square Root of a Number Squared
Please enter another number to calculate the square root of the number squared.

Square Root of 501 Squared
Here is the next number on our list for which we have calculated the square root of the number squared.

Note: Decimal numbers on this page are rounded to the nearest ten-thousandths if necessary.