Square Root of 505 Squared (√505^2)

Square Root of 505 Squared

Here we will discuss and calculate the square root of 505 squared. The problem in mathematical terms that we want to solve is displayed below:

√505²

We are doing two math operations: The radical sign √ means that you are taking the square root of 505 and the ² means to square 505. 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 505. Nevertheless, read on because we will show you different ways of calculating the square root of 505 squared to prove that the answer is 505.

We start by first taking the square root of 505 and then square that result to get our answer like this:

√505 = 22.4722

22.4722² = 505

Now, we will do the operations in opposite order where we first square 505 and then calculate the square root of the result:

505² = 255025

√255025 = 505

You may also find this math rule interesting when dealing with a problem like the square root of 505 squared:

√x² = √x · √x

It also proves that the square root of 505 squared equals 505.

√505² = √505 · √505

√505 · √505 = 22.4722 · 22.4722

22.4722 · 22.4722 = 505

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