Square Root of 478 Squared (√478^2)

Square Root of 478 Squared

Here we will discuss and calculate the square root of 478 squared. The problem in mathematical terms that we want to solve is displayed below:

√478²

We are doing two math operations: The radical sign √ means that you are taking the square root of 478 and the ² means to square 478. 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 478. Nevertheless, read on because we will show you different ways of calculating the square root of 478 squared to prove that the answer is 478.

We start by first taking the square root of 478 and then square that result to get our answer like this:

√478 = 21.8632

21.8632² = 478

Now, we will do the operations in opposite order where we first square 478 and then calculate the square root of the result:

478² = 228484

√228484 = 478

You may also find this math rule interesting when dealing with a problem like the square root of 478 squared:

√x² = √x · √x

It also proves that the square root of 478 squared equals 478.

√478² = √478 · √478

√478 · √478 = 21.8632 · 21.8632

21.8632 · 21.8632 = 478

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