Simplify Square Root of 40225

Here we will show you two methods that you can use to simplify the square root of 40225. In other words, we will show you how to find the square root of 40225 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.

√40225 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40225 to simplify the square root of 40225. 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 40225. The factors of 40225 are 1, 5, 25, 1609, 8045, and 40225. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 40225 divided by the greatest perfect square from the list of all factors of 40225. We determined above that the greatest perfect square from the list of all factors of 40225 is 25. Furthermore, 40225 divided by 25 is 1609, therefore B equals 1609.

Now we have A and B and can get our answer to 40225 in its simplest radical form as follows:

√40225 = A√B

√40225 = 5√1609

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40225 to simplify the square root of 40225 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 40225 and then take the square root of that product. The prime factors that multiply together to make 40225 are 5 x 5 x 1609. 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 40225 by the number (A) squared. 5 squared is 25 and 40225 divided by 25 is 1609. Therefore, B equals 1609.

Once again we have A and B and can get our answer to 40225 in its simplest radical form as follows:

√40225 = A√B

√40225 = 5√1609

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Simplify Square Root of 40226
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