Simplify Square Root of 12250

Here we will show you two methods that you can use to simplify the square root of 12250. In other words, we will show you how to find the square root of 12250 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.

√12250 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12250 to simplify the square root of 12250. 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 12250. The factors of 12250 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 125, 175, 245, 250, 350, 490, 875, 1225, 1750, 2450, 6125, and 12250. Furthermore, the greatest perfect square on this list is 1225 and the square root of 1225 is 35. Therefore, A equals 35.

B = Calculate 12250 divided by the greatest perfect square from the list of all factors of 12250. We determined above that the greatest perfect square from the list of all factors of 12250 is 1225. Furthermore, 12250 divided by 1225 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 12250 in its simplest radical form as follows:

√12250 = A√B

√12250 = 35√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12250 to simplify the square root of 12250 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 12250 and then take the square root of that product. The prime factors that multiply together to make 12250 are 2 x 5 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 5 x 5 x 7 x 7 = 1225 and the square root of 1225 is 35. Therefore, A equals 35.

B = Divide 12250 by the number (A) squared. 35 squared is 1225 and 12250 divided by 1225 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 12250 in its simplest radical form as follows:

√12250 = A√B

√12250 = 35√10

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Simplify Square Root of 12251
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