Simplify Square Root of 64500

Here we will show you two methods that you can use to simplify the square root of 64500. In other words, we will show you how to find the square root of 64500 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.

√64500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64500 to simplify the square root of 64500. 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 64500. The factors of 64500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 43, 50, 60, 75, 86, 100, 125, 129, 150, 172, 215, 250, 258, 300, 375, 430, 500, 516, 645, 750, 860, 1075, 1290, 1500, 2150, 2580, 3225, 4300, 5375, 6450, 10750, 12900, 16125, 21500, 32250, and 64500. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 64500 divided by the greatest perfect square from the list of all factors of 64500. We determined above that the greatest perfect square from the list of all factors of 64500 is 100. Furthermore, 64500 divided by 100 is 645, therefore B equals 645.

Now we have A and B and can get our answer to 64500 in its simplest radical form as follows:

√64500 = A√B

√64500 = 10√645

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64500 to simplify the square root of 64500 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 64500 and then take the square root of that product. The prime factors that multiply together to make 64500 are 2 x 2 x 3 x 5 x 5 x 5 x 43. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 64500 by the number (A) squared. 10 squared is 100 and 64500 divided by 100 is 645. Therefore, B equals 645.

Once again we have A and B and can get our answer to 64500 in its simplest radical form as follows:

√64500 = A√B

√64500 = 10√645

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