Simplify Square Root of 89364

Here we will show you two methods that you can use to simplify the square root of 89364. In other words, we will show you how to find the square root of 89364 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.

√89364 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89364 to simplify the square root of 89364. 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 89364. The factors of 89364 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 677, 1354, 2031, 2708, 4062, 7447, 8124, 14894, 22341, 29788, 44682, and 89364. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 89364 divided by the greatest perfect square from the list of all factors of 89364. We determined above that the greatest perfect square from the list of all factors of 89364 is 4. Furthermore, 89364 divided by 4 is 22341, therefore B equals 22341.

Now we have A and B and can get our answer to 89364 in its simplest radical form as follows:

√89364 = A√B

√89364 = 2√22341

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89364 to simplify the square root of 89364 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 89364 and then take the square root of that product. The prime factors that multiply together to make 89364 are 2 x 2 x 3 x 11 x 677. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 89364 by the number (A) squared. 2 squared is 4 and 89364 divided by 4 is 22341. Therefore, B equals 22341.

Once again we have A and B and can get our answer to 89364 in its simplest radical form as follows:

√89364 = A√B

√89364 = 2√22341

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Simplify Square Root of 89365
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