Simplify Square Root of 58275

Here we will show you two methods that you can use to simplify the square root of 58275. In other words, we will show you how to find the square root of 58275 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.

√58275 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58275 to simplify the square root of 58275. 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 58275. The factors of 58275 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 37, 45, 63, 75, 105, 111, 175, 185, 225, 259, 315, 333, 525, 555, 777, 925, 1295, 1575, 1665, 2331, 2775, 3885, 6475, 8325, 11655, 19425, and 58275. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 58275 divided by the greatest perfect square from the list of all factors of 58275. We determined above that the greatest perfect square from the list of all factors of 58275 is 225. Furthermore, 58275 divided by 225 is 259, therefore B equals 259.

Now we have A and B and can get our answer to 58275 in its simplest radical form as follows:

√58275 = A√B

√58275 = 15√259

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58275 to simplify the square root of 58275 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 58275 and then take the square root of that product. The prime factors that multiply together to make 58275 are 3 x 3 x 5 x 5 x 7 x 37. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 58275 by the number (A) squared. 15 squared is 225 and 58275 divided by 225 is 259. Therefore, B equals 259.

Once again we have A and B and can get our answer to 58275 in its simplest radical form as follows:

√58275 = A√B

√58275 = 15√259

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Simplify Square Root of 58276
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