Simplify Square Root of 19525

Here we will show you two methods that you can use to simplify the square root of 19525. In other words, we will show you how to find the square root of 19525 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.

√19525 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19525 to simplify the square root of 19525. 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 19525. The factors of 19525 are 1, 5, 11, 25, 55, 71, 275, 355, 781, 1775, 3905, and 19525. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 19525 divided by the greatest perfect square from the list of all factors of 19525. We determined above that the greatest perfect square from the list of all factors of 19525 is 25. Furthermore, 19525 divided by 25 is 781, therefore B equals 781.

Now we have A and B and can get our answer to 19525 in its simplest radical form as follows:

√19525 = A√B

√19525 = 5√781

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19525 to simplify the square root of 19525 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 19525 and then take the square root of that product. The prime factors that multiply together to make 19525 are 5 x 5 x 11 x 71. 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 19525 by the number (A) squared. 5 squared is 25 and 19525 divided by 25 is 781. Therefore, B equals 781.

Once again we have A and B and can get our answer to 19525 in its simplest radical form as follows:

√19525 = A√B

√19525 = 5√781

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Simplify Square Root of 19526
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