Square Root of 513 Squared (√513^2)

Square Root of 513 Squared

Here we will discuss and calculate the square root of 513 squared. The problem in mathematical terms that we want to solve is displayed below:

√513²

We are doing two math operations: The radical sign √ means that you are taking the square root of 513 and the ² means to square 513. 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 513. Nevertheless, read on because we will show you different ways of calculating the square root of 513 squared to prove that the answer is 513.

We start by first taking the square root of 513 and then square that result to get our answer like this:

√513 = 22.6495

22.6495² = 513

Now, we will do the operations in opposite order where we first square 513 and then calculate the square root of the result:

513² = 263169

√263169 = 513

You may also find this math rule interesting when dealing with a problem like the square root of 513 squared:

√x² = √x · √x

It also proves that the square root of 513 squared equals 513.

√513² = √513 · √513

√513 · √513 = 22.6495 · 22.6495

22.6495 · 22.6495 = 513

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