Simplify Square Root of 36897

Here we will show you two methods that you can use to simplify the square root of 36897. In other words, we will show you how to find the square root of 36897 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.

√36897 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36897 to simplify the square root of 36897. 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 36897. The factors of 36897 are 1, 3, 7, 21, 49, 147, 251, 753, 1757, 5271, 12299, and 36897. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 36897 divided by the greatest perfect square from the list of all factors of 36897. We determined above that the greatest perfect square from the list of all factors of 36897 is 49. Furthermore, 36897 divided by 49 is 753, therefore B equals 753.

Now we have A and B and can get our answer to 36897 in its simplest radical form as follows:

√36897 = A√B

√36897 = 7√753

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36897 to simplify the square root of 36897 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 36897 and then take the square root of that product. The prime factors that multiply together to make 36897 are 3 x 7 x 7 x 251. 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 36897 by the number (A) squared. 7 squared is 49 and 36897 divided by 49 is 753. Therefore, B equals 753.

Once again we have A and B and can get our answer to 36897 in its simplest radical form as follows:

√36897 = A√B

√36897 = 7√753

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Simplify Square Root of 36898
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