Simplify Square Root of 48020

Here we will show you two methods that you can use to simplify the square root of 48020. In other words, we will show you how to find the square root of 48020 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.

√48020 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48020 to simplify the square root of 48020. 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 48020. The factors of 48020 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 343, 490, 686, 980, 1372, 1715, 2401, 3430, 4802, 6860, 9604, 12005, 24010, and 48020. Furthermore, the greatest perfect square on this list is 9604 and the square root of 9604 is 98. Therefore, A equals 98.

B = Calculate 48020 divided by the greatest perfect square from the list of all factors of 48020. We determined above that the greatest perfect square from the list of all factors of 48020 is 9604. Furthermore, 48020 divided by 9604 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 48020 in its simplest radical form as follows:

√48020 = A√B

√48020 = 98√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48020 to simplify the square root of 48020 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 48020 and then take the square root of that product. The prime factors that multiply together to make 48020 are 2 x 2 x 5 x 7 x 7 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 7 x 7 x 7 x 7 = 9604 and the square root of 9604 is 98. Therefore, A equals 98.

B = Divide 48020 by the number (A) squared. 98 squared is 9604 and 48020 divided by 9604 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 48020 in its simplest radical form as follows:

√48020 = A√B

√48020 = 98√5

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