Simplify Square Root of 15000

Here we will show you two methods that you can use to simplify the square root of 15000. In other words, we will show you how to find the square root of 15000 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.

√15000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15000 to simplify the square root of 15000. 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 15000. The factors of 15000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 625, 750, 1000, 1250, 1500, 1875, 2500, 3000, 3750, 5000, 7500, and 15000. Furthermore, the greatest perfect square on this list is 2500 and the square root of 2500 is 50. Therefore, A equals 50.

B = Calculate 15000 divided by the greatest perfect square from the list of all factors of 15000. We determined above that the greatest perfect square from the list of all factors of 15000 is 2500. Furthermore, 15000 divided by 2500 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 15000 in its simplest radical form as follows:

√15000 = A√B

√15000 = 50√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15000 to simplify the square root of 15000 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 15000 and then take the square root of that product. The prime factors that multiply together to make 15000 are 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 5 x 5 = 2500 and the square root of 2500 is 50. Therefore, A equals 50.

B = Divide 15000 by the number (A) squared. 50 squared is 2500 and 15000 divided by 2500 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 15000 in its simplest radical form as follows:

√15000 = A√B

√15000 = 50√6

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Simplify Square Root of 15001
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