Simplify Square Root of 14750

Here we will show you two methods that you can use to simplify the square root of 14750. In other words, we will show you how to find the square root of 14750 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.

√14750 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 14750 to simplify the square root of 14750. 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 14750. The factors of 14750 are 1, 2, 5, 10, 25, 50, 59, 118, 125, 250, 295, 590, 1475, 2950, 7375, and 14750. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 14750 divided by the greatest perfect square from the list of all factors of 14750. We determined above that the greatest perfect square from the list of all factors of 14750 is 25. Furthermore, 14750 divided by 25 is 590, therefore B equals 590.

Now we have A and B and can get our answer to 14750 in its simplest radical form as follows:

√14750 = A√B

√14750 = 5√590

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 14750 to simplify the square root of 14750 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 14750 and then take the square root of that product. The prime factors that multiply together to make 14750 are 2 x 5 x 5 x 5 x 59. 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 14750 by the number (A) squared. 5 squared is 25 and 14750 divided by 25 is 590. Therefore, B equals 590.

Once again we have A and B and can get our answer to 14750 in its simplest radical form as follows:

√14750 = A√B

√14750 = 5√590

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Simplify Square Root of 14751
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