Simplify Square Root of 89425

Here we will show you two methods that you can use to simplify the square root of 89425. In other words, we will show you how to find the square root of 89425 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.

√89425 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89425 to simplify the square root of 89425. 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 89425. The factors of 89425 are 1, 5, 7, 25, 35, 49, 73, 175, 245, 365, 511, 1225, 1825, 2555, 3577, 12775, 17885, and 89425. Furthermore, the greatest perfect square on this list is 1225 and the square root of 1225 is 35. Therefore, A equals 35.

B = Calculate 89425 divided by the greatest perfect square from the list of all factors of 89425. We determined above that the greatest perfect square from the list of all factors of 89425 is 1225. Furthermore, 89425 divided by 1225 is 73, therefore B equals 73.

Now we have A and B and can get our answer to 89425 in its simplest radical form as follows:

√89425 = A√B

√89425 = 35√73

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89425 to simplify the square root of 89425 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 89425 and then take the square root of that product. The prime factors that multiply together to make 89425 are 5 x 5 x 7 x 7 x 73. 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 89425 by the number (A) squared. 35 squared is 1225 and 89425 divided by 1225 is 73. Therefore, B equals 73.

Once again we have A and B and can get our answer to 89425 in its simplest radical form as follows:

√89425 = A√B

√89425 = 35√73

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Simplify Square Root of 89426
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