Simplify Square Root of 18880

Here we will show you two methods that you can use to simplify the square root of 18880. In other words, we will show you how to find the square root of 18880 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.

√18880 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18880 to simplify the square root of 18880. 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 18880. The factors of 18880 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 59, 64, 80, 118, 160, 236, 295, 320, 472, 590, 944, 1180, 1888, 2360, 3776, 4720, 9440, and 18880. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 18880 divided by the greatest perfect square from the list of all factors of 18880. We determined above that the greatest perfect square from the list of all factors of 18880 is 64. Furthermore, 18880 divided by 64 is 295, therefore B equals 295.

Now we have A and B and can get our answer to 18880 in its simplest radical form as follows:

√18880 = A√B

√18880 = 8√295

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18880 to simplify the square root of 18880 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 18880 and then take the square root of that product. The prime factors that multiply together to make 18880 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 59. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 18880 by the number (A) squared. 8 squared is 64 and 18880 divided by 64 is 295. Therefore, B equals 295.

Once again we have A and B and can get our answer to 18880 in its simplest radical form as follows:

√18880 = A√B

√18880 = 8√295

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Simplify Square Root of 18881
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