Simplify Square Root of 64480

Here we will show you two methods that you can use to simplify the square root of 64480. In other words, we will show you how to find the square root of 64480 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.

√64480 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64480 to simplify the square root of 64480. 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 64480. The factors of 64480 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 31, 32, 40, 52, 62, 65, 80, 104, 124, 130, 155, 160, 208, 248, 260, 310, 403, 416, 496, 520, 620, 806, 992, 1040, 1240, 1612, 2015, 2080, 2480, 3224, 4030, 4960, 6448, 8060, 12896, 16120, 32240, and 64480. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 64480 divided by the greatest perfect square from the list of all factors of 64480. We determined above that the greatest perfect square from the list of all factors of 64480 is 16. Furthermore, 64480 divided by 16 is 4030, therefore B equals 4030.

Now we have A and B and can get our answer to 64480 in its simplest radical form as follows:

√64480 = A√B

√64480 = 4√4030

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64480 to simplify the square root of 64480 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 64480 and then take the square root of that product. The prime factors that multiply together to make 64480 are 2 x 2 x 2 x 2 x 2 x 5 x 13 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 64480 by the number (A) squared. 4 squared is 16 and 64480 divided by 16 is 4030. Therefore, B equals 4030.

Once again we have A and B and can get our answer to 64480 in its simplest radical form as follows:

√64480 = A√B

√64480 = 4√4030

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