Simplify Square Root of 73515

Here we will show you two methods that you can use to simplify the square root of 73515. In other words, we will show you how to find the square root of 73515 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.

√73515 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73515 to simplify the square root of 73515. 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 73515. The factors of 73515 are 1, 3, 5, 13, 15, 29, 39, 65, 87, 145, 169, 195, 377, 435, 507, 845, 1131, 1885, 2535, 4901, 5655, 14703, 24505, and 73515. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 73515 divided by the greatest perfect square from the list of all factors of 73515. We determined above that the greatest perfect square from the list of all factors of 73515 is 169. Furthermore, 73515 divided by 169 is 435, therefore B equals 435.

Now we have A and B and can get our answer to 73515 in its simplest radical form as follows:

√73515 = A√B

√73515 = 13√435

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73515 to simplify the square root of 73515 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 73515 and then take the square root of that product. The prime factors that multiply together to make 73515 are 3 x 5 x 13 x 13 x 29. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 73515 by the number (A) squared. 13 squared is 169 and 73515 divided by 169 is 435. Therefore, B equals 435.

Once again we have A and B and can get our answer to 73515 in its simplest radical form as follows:

√73515 = A√B

√73515 = 13√435

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Simplify Square Root of 73516
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