Simplify Square Root of 54450

Here we will show you two methods that you can use to simplify the square root of 54450. In other words, we will show you how to find the square root of 54450 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√54450 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54450 to simplify the square root of 54450. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 54450. The factors of 54450 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 25, 30, 33, 45, 50, 55, 66, 75, 90, 99, 110, 121, 150, 165, 198, 225, 242, 275, 330, 363, 450, 495, 550, 605, 726, 825, 990, 1089, 1210, 1650, 1815, 2178, 2475, 3025, 3630, 4950, 5445, 6050, 9075, 10890, 18150, 27225, and 54450. Furthermore, the greatest perfect square on this list is 27225 and the square root of 27225 is 165. Therefore, A equals 165.

B = Calculate 54450 divided by the greatest perfect square from the list of all factors of 54450. We determined above that the greatest perfect square from the list of all factors of 54450 is 27225. Furthermore, 54450 divided by 27225 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 54450 in its simplest radical form as follows:

√54450 = A√B

√54450 = 165√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54450 to simplify the square root of 54450 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 54450 and then take the square root of that product. The prime factors that multiply together to make 54450 are 2 x 3 x 3 x 5 x 5 x 11 x 11. When we strip out the pairs only, we get 3 x 3 x 5 x 5 x 11 x 11 = 27225 and the square root of 27225 is 165. Therefore, A equals 165.

B = Divide 54450 by the number (A) squared. 165 squared is 27225 and 54450 divided by 27225 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 54450 in its simplest radical form as follows:

√54450 = A√B

√54450 = 165√2

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 54451
Here is the next square root on our list that we have simplifed for you.