Simplify Square Root of 23475

Here we will show you two methods that you can use to simplify the square root of 23475. In other words, we will show you how to find the square root of 23475 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.

√23475 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23475 to simplify the square root of 23475. 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 23475. The factors of 23475 are 1, 3, 5, 15, 25, 75, 313, 939, 1565, 4695, 7825, and 23475. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 23475 divided by the greatest perfect square from the list of all factors of 23475. We determined above that the greatest perfect square from the list of all factors of 23475 is 25. Furthermore, 23475 divided by 25 is 939, therefore B equals 939.

Now we have A and B and can get our answer to 23475 in its simplest radical form as follows:

√23475 = A√B

√23475 = 5√939

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23475 to simplify the square root of 23475 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 23475 and then take the square root of that product. The prime factors that multiply together to make 23475 are 3 x 5 x 5 x 313. 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 23475 by the number (A) squared. 5 squared is 25 and 23475 divided by 25 is 939. Therefore, B equals 939.

Once again we have A and B and can get our answer to 23475 in its simplest radical form as follows:

√23475 = A√B

√23475 = 5√939

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Simplify Square Root of 23476
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