Simplify Square Root of 88360

Here we will show you two methods that you can use to simplify the square root of 88360. In other words, we will show you how to find the square root of 88360 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.

√88360 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88360 to simplify the square root of 88360. 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 88360. The factors of 88360 are 1, 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, 940, 1880, 2209, 4418, 8836, 11045, 17672, 22090, 44180, and 88360. Furthermore, the greatest perfect square on this list is 8836 and the square root of 8836 is 94. Therefore, A equals 94.

B = Calculate 88360 divided by the greatest perfect square from the list of all factors of 88360. We determined above that the greatest perfect square from the list of all factors of 88360 is 8836. Furthermore, 88360 divided by 8836 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 88360 in its simplest radical form as follows:

√88360 = A√B

√88360 = 94√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88360 to simplify the square root of 88360 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 88360 and then take the square root of that product. The prime factors that multiply together to make 88360 are 2 x 2 x 2 x 5 x 47 x 47. When we strip out the pairs only, we get 2 x 2 x 47 x 47 = 8836 and the square root of 8836 is 94. Therefore, A equals 94.

B = Divide 88360 by the number (A) squared. 94 squared is 8836 and 88360 divided by 8836 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 88360 in its simplest radical form as follows:

√88360 = A√B

√88360 = 94√10

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Simplify Square Root of 88361
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