Simplify Square Root of 36358

Here we will show you two methods that you can use to simplify the square root of 36358. In other words, we will show you how to find the square root of 36358 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.

√36358 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36358 to simplify the square root of 36358. 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 36358. The factors of 36358 are 1, 2, 7, 14, 49, 53, 98, 106, 343, 371, 686, 742, 2597, 5194, 18179, and 36358. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 36358 divided by the greatest perfect square from the list of all factors of 36358. We determined above that the greatest perfect square from the list of all factors of 36358 is 49. Furthermore, 36358 divided by 49 is 742, therefore B equals 742.

Now we have A and B and can get our answer to 36358 in its simplest radical form as follows:

√36358 = A√B

√36358 = 7√742

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36358 to simplify the square root of 36358 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 36358 and then take the square root of that product. The prime factors that multiply together to make 36358 are 2 x 7 x 7 x 7 x 53. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 36358 by the number (A) squared. 7 squared is 49 and 36358 divided by 49 is 742. Therefore, B equals 742.

Once again we have A and B and can get our answer to 36358 in its simplest radical form as follows:

√36358 = A√B

√36358 = 7√742

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Simplify Square Root of 36359
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