Simplify Square Root of 47610

Here we will show you two methods that you can use to simplify the square root of 47610. In other words, we will show you how to find the square root of 47610 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.

√47610 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 47610 to simplify the square root of 47610. 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 47610. The factors of 47610 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 30, 45, 46, 69, 90, 115, 138, 207, 230, 345, 414, 529, 690, 1035, 1058, 1587, 2070, 2645, 3174, 4761, 5290, 7935, 9522, 15870, 23805, and 47610. Furthermore, the greatest perfect square on this list is 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Calculate 47610 divided by the greatest perfect square from the list of all factors of 47610. We determined above that the greatest perfect square from the list of all factors of 47610 is 4761. Furthermore, 47610 divided by 4761 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 47610 in its simplest radical form as follows:

√47610 = A√B

√47610 = 69√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 47610 to simplify the square root of 47610 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 47610 and then take the square root of that product. The prime factors that multiply together to make 47610 are 2 x 3 x 3 x 5 x 23 x 23. When we strip out the pairs only, we get 3 x 3 x 23 x 23 = 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Divide 47610 by the number (A) squared. 69 squared is 4761 and 47610 divided by 4761 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 47610 in its simplest radical form as follows:

√47610 = A√B

√47610 = 69√10

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