Simplify Square Root of 46708

Here we will show you two methods that you can use to simplify the square root of 46708. In other words, we will show you how to find the square root of 46708 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.

√46708 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 46708 to simplify the square root of 46708. 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 46708. The factors of 46708 are 1, 2, 4, 11677, 23354, and 46708. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 46708 divided by the greatest perfect square from the list of all factors of 46708. We determined above that the greatest perfect square from the list of all factors of 46708 is 4. Furthermore, 46708 divided by 4 is 11677, therefore B equals 11677.

Now we have A and B and can get our answer to 46708 in its simplest radical form as follows:

√46708 = A√B

√46708 = 2√11677

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 46708 to simplify the square root of 46708 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 46708 and then take the square root of that product. The prime factors that multiply together to make 46708 are 2 x 2 x 11677. 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 46708 by the number (A) squared. 2 squared is 4 and 46708 divided by 4 is 11677. Therefore, B equals 11677.

Once again we have A and B and can get our answer to 46708 in its simplest radical form as follows:

√46708 = A√B

√46708 = 2√11677

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Simplify Square Root of 46709
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