Square Root of 1003 Squared (√1003^2)

Square Root of 1003 Squared

Here we will discuss and calculate the square root of 1003 squared. The problem in mathematical terms that we want to solve is displayed below:

√1003²

We are doing two math operations: The radical sign √ means that you are taking the square root of 1003 and the ² means to square 1003. 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 1003. Nevertheless, read on because we will show you different ways of calculating the square root of 1003 squared to prove that the answer is 1003.

We start by first taking the square root of 1003 and then square that result to get our answer like this:

√1003 = 31.6702

31.6702² = 1003

Now, we will do the operations in opposite order where we first square 1003 and then calculate the square root of the result:

1003² = 1006009

√1006009 = 1003

You may also find this math rule interesting when dealing with a problem like the square root of 1003 squared:

√x² = √x · √x

It also proves that the square root of 1003 squared equals 1003.

√1003² = √1003 · √1003

√1003 · √1003 = 31.6702 · 31.6702

31.6702 · 31.6702 = 1003

Square Root of a Number Squared
Please enter another number to calculate the square root of the number squared.

Square Root of 1004 Squared
Here is the next number on our list for which we have calculated the square root of the number squared.

Note: Decimal numbers on this page are rounded to the nearest ten-thousandths if necessary.