Square Root of 5000 Squared (√5000^2)

Square Root of 5000 Squared

Here we will discuss and calculate the square root of 5000 squared. The problem in mathematical terms that we want to solve is displayed below:

√5000²

We are doing two math operations: The radical sign √ means that you are taking the square root of 5000 and the ² means to square 5000. 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 5000. Nevertheless, read on because we will show you different ways of calculating the square root of 5000 squared to prove that the answer is 5000.

We start by first taking the square root of 5000 and then square that result to get our answer like this:

√5000 = 70.7107

70.7107² = 5000

Now, we will do the operations in opposite order where we first square 5000 and then calculate the square root of the result:

5000² = 25000000

√25000000 = 5000

You may also find this math rule interesting when dealing with a problem like the square root of 5000 squared:

√x² = √x · √x

It also proves that the square root of 5000 squared equals 5000.

√5000² = √5000 · √5000

√5000 · √5000 = 70.7107 · 70.7107

70.7107 · 70.7107 = 5000

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