Simplify Square Root of 54150

Here we will show you two methods that you can use to simplify the square root of 54150. In other words, we will show you how to find the square root of 54150 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.

√54150 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54150 to simplify the square root of 54150. 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 54150. The factors of 54150 are 1, 2, 3, 5, 6, 10, 15, 19, 25, 30, 38, 50, 57, 75, 95, 114, 150, 190, 285, 361, 475, 570, 722, 950, 1083, 1425, 1805, 2166, 2850, 3610, 5415, 9025, 10830, 18050, 27075, and 54150. Furthermore, the greatest perfect square on this list is 9025 and the square root of 9025 is 95. Therefore, A equals 95.

B = Calculate 54150 divided by the greatest perfect square from the list of all factors of 54150. We determined above that the greatest perfect square from the list of all factors of 54150 is 9025. Furthermore, 54150 divided by 9025 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 54150 in its simplest radical form as follows:

√54150 = A√B

√54150 = 95√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54150 to simplify the square root of 54150 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 54150 and then take the square root of that product. The prime factors that multiply together to make 54150 are 2 x 3 x 5 x 5 x 19 x 19. When we strip out the pairs only, we get 5 x 5 x 19 x 19 = 9025 and the square root of 9025 is 95. Therefore, A equals 95.

B = Divide 54150 by the number (A) squared. 95 squared is 9025 and 54150 divided by 9025 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 54150 in its simplest radical form as follows:

√54150 = A√B

√54150 = 95√6

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