Simplify Square Root of 58650

Here we will show you two methods that you can use to simplify the square root of 58650. In other words, we will show you how to find the square root of 58650 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.

√58650 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58650 to simplify the square root of 58650. 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 58650. The factors of 58650 are 1, 2, 3, 5, 6, 10, 15, 17, 23, 25, 30, 34, 46, 50, 51, 69, 75, 85, 102, 115, 138, 150, 170, 230, 255, 345, 391, 425, 510, 575, 690, 782, 850, 1150, 1173, 1275, 1725, 1955, 2346, 2550, 3450, 3910, 5865, 9775, 11730, 19550, 29325, and 58650. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 58650 divided by the greatest perfect square from the list of all factors of 58650. We determined above that the greatest perfect square from the list of all factors of 58650 is 25. Furthermore, 58650 divided by 25 is 2346, therefore B equals 2346.

Now we have A and B and can get our answer to 58650 in its simplest radical form as follows:

√58650 = A√B

√58650 = 5√2346

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58650 to simplify the square root of 58650 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 58650 and then take the square root of that product. The prime factors that multiply together to make 58650 are 2 x 3 x 5 x 5 x 17 x 23. 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 58650 by the number (A) squared. 5 squared is 25 and 58650 divided by 25 is 2346. Therefore, B equals 2346.

Once again we have A and B and can get our answer to 58650 in its simplest radical form as follows:

√58650 = A√B

√58650 = 5√2346

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