Square Root of 684 Squared (√684^2)

Square Root of 684 Squared

Here we will discuss and calculate the square root of 684 squared. The problem in mathematical terms that we want to solve is displayed below:

√684²

We are doing two math operations: The radical sign √ means that you are taking the square root of 684 and the ² means to square 684. 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 684. Nevertheless, read on because we will show you different ways of calculating the square root of 684 squared to prove that the answer is 684.

We start by first taking the square root of 684 and then square that result to get our answer like this:

√684 = 26.1534

26.1534² = 684

Now, we will do the operations in opposite order where we first square 684 and then calculate the square root of the result:

684² = 467856

√467856 = 684

You may also find this math rule interesting when dealing with a problem like the square root of 684 squared:

√x² = √x · √x

It also proves that the square root of 684 squared equals 684.

√684² = √684 · √684

√684 · √684 = 26.1534 · 26.1534

26.1534 · 26.1534 = 684

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