Simplify Square Root of 42525

Here we will show you two methods that you can use to simplify the square root of 42525. In other words, we will show you how to find the square root of 42525 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.

√42525 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42525 to simplify the square root of 42525. 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 42525. The factors of 42525 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 81, 105, 135, 175, 189, 225, 243, 315, 405, 525, 567, 675, 945, 1215, 1575, 1701, 2025, 2835, 4725, 6075, 8505, 14175, and 42525. Furthermore, the greatest perfect square on this list is 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Calculate 42525 divided by the greatest perfect square from the list of all factors of 42525. We determined above that the greatest perfect square from the list of all factors of 42525 is 2025. Furthermore, 42525 divided by 2025 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 42525 in its simplest radical form as follows:

√42525 = A√B

√42525 = 45√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42525 to simplify the square root of 42525 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 42525 and then take the square root of that product. The prime factors that multiply together to make 42525 are 3 x 3 x 3 x 3 x 3 x 5 x 5 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 5 x 5 = 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Divide 42525 by the number (A) squared. 45 squared is 2025 and 42525 divided by 2025 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 42525 in its simplest radical form as follows:

√42525 = A√B

√42525 = 45√21

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Simplify Square Root of 42526
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