Square Root of 1689 Squared (√1689^2)

Square Root of 1689 Squared

Here we will discuss and calculate the square root of 1689 squared. The problem in mathematical terms that we want to solve is displayed below:

√1689²

We are doing two math operations: The radical sign √ means that you are taking the square root of 1689 and the ² means to square 1689. 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 1689. Nevertheless, read on because we will show you different ways of calculating the square root of 1689 squared to prove that the answer is 1689.

We start by first taking the square root of 1689 and then square that result to get our answer like this:

√1689 = 41.0974

41.0974² = 1689

Now, we will do the operations in opposite order where we first square 1689 and then calculate the square root of the result:

1689² = 2852721

√2852721 = 1689

You may also find this math rule interesting when dealing with a problem like the square root of 1689 squared:

√x² = √x · √x

It also proves that the square root of 1689 squared equals 1689.

√1689² = √1689 · √1689

√1689 · √1689 = 41.0974 · 41.0974

41.0974 · 41.0974 = 1689

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