Simplify Square Root of 72125

Here we will show you two methods that you can use to simplify the square root of 72125. In other words, we will show you how to find the square root of 72125 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.

√72125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72125 to simplify the square root of 72125. 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 72125. The factors of 72125 are 1, 5, 25, 125, 577, 2885, 14425, and 72125. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 72125 divided by the greatest perfect square from the list of all factors of 72125. We determined above that the greatest perfect square from the list of all factors of 72125 is 25. Furthermore, 72125 divided by 25 is 2885, therefore B equals 2885.

Now we have A and B and can get our answer to 72125 in its simplest radical form as follows:

√72125 = A√B

√72125 = 5√2885

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72125 to simplify the square root of 72125 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 72125 and then take the square root of that product. The prime factors that multiply together to make 72125 are 5 x 5 x 5 x 577. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 72125 by the number (A) squared. 5 squared is 25 and 72125 divided by 25 is 2885. Therefore, B equals 2885.

Once again we have A and B and can get our answer to 72125 in its simplest radical form as follows:

√72125 = A√B

√72125 = 5√2885

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Simplify Square Root of 72126
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