Simplify Square Root of 40825

Here we will show you two methods that you can use to simplify the square root of 40825. In other words, we will show you how to find the square root of 40825 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.

√40825 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40825 to simplify the square root of 40825. 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 40825. The factors of 40825 are 1, 5, 23, 25, 71, 115, 355, 575, 1633, 1775, 8165, and 40825. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 40825 divided by the greatest perfect square from the list of all factors of 40825. We determined above that the greatest perfect square from the list of all factors of 40825 is 25. Furthermore, 40825 divided by 25 is 1633, therefore B equals 1633.

Now we have A and B and can get our answer to 40825 in its simplest radical form as follows:

√40825 = A√B

√40825 = 5√1633

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40825 to simplify the square root of 40825 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 40825 and then take the square root of that product. The prime factors that multiply together to make 40825 are 5 x 5 x 23 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 40825 by the number (A) squared. 5 squared is 25 and 40825 divided by 25 is 1633. Therefore, B equals 1633.

Once again we have A and B and can get our answer to 40825 in its simplest radical form as follows:

√40825 = A√B

√40825 = 5√1633

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Simplify Square Root of 40826
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