Simplify Square Root of 26010

Here we will show you two methods that you can use to simplify the square root of 26010. In other words, we will show you how to find the square root of 26010 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.

√26010 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26010 to simplify the square root of 26010. 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 26010. The factors of 26010 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 289, 306, 510, 578, 765, 867, 1445, 1530, 1734, 2601, 2890, 4335, 5202, 8670, 13005, and 26010. Furthermore, the greatest perfect square on this list is 2601 and the square root of 2601 is 51. Therefore, A equals 51.

B = Calculate 26010 divided by the greatest perfect square from the list of all factors of 26010. We determined above that the greatest perfect square from the list of all factors of 26010 is 2601. Furthermore, 26010 divided by 2601 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 26010 in its simplest radical form as follows:

√26010 = A√B

√26010 = 51√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26010 to simplify the square root of 26010 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 26010 and then take the square root of that product. The prime factors that multiply together to make 26010 are 2 x 3 x 3 x 5 x 17 x 17. When we strip out the pairs only, we get 3 x 3 x 17 x 17 = 2601 and the square root of 2601 is 51. Therefore, A equals 51.

B = Divide 26010 by the number (A) squared. 51 squared is 2601 and 26010 divided by 2601 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 26010 in its simplest radical form as follows:

√26010 = A√B

√26010 = 51√10

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Simplify Square Root of 26011
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