Simplify Square Root of 180

Here we will show you two methods that you can use to simplify the square root of 180. In other words, we will show you how to find the square root of 180 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.

√180 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 180 to simplify the square root of 180. 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 180. The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 180 divided by the greatest perfect square from the list of all factors of 180. We determined above that the greatest perfect square from the list of all factors of 180 is 36. Furthermore, 180 divided by 36 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 180 in its simplest radical form as follows:

√180 = A√B

√180 = 6√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 180 to simplify the square root of 180 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 180 and then take the square root of that product. The prime factors that multiply together to make 180 are 2 x 2 x 3 x 3 x 5. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 180 by the number (A) squared. 6 squared is 36 and 180 divided by 36 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 180 in its simplest radical form as follows:

√180 = A√B

√180 = 6√5

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Simplify Square Root of 181
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