Simplify Square Root of 43758

Here we will show you two methods that you can use to simplify the square root of 43758. In other words, we will show you how to find the square root of 43758 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.

√43758 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43758 to simplify the square root of 43758. 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 43758. The factors of 43758 are 1, 2, 3, 6, 9, 11, 13, 17, 18, 22, 26, 33, 34, 39, 51, 66, 78, 99, 102, 117, 143, 153, 187, 198, 221, 234, 286, 306, 374, 429, 442, 561, 663, 858, 1122, 1287, 1326, 1683, 1989, 2431, 2574, 3366, 3978, 4862, 7293, 14586, 21879, and 43758. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 43758 divided by the greatest perfect square from the list of all factors of 43758. We determined above that the greatest perfect square from the list of all factors of 43758 is 9. Furthermore, 43758 divided by 9 is 4862, therefore B equals 4862.

Now we have A and B and can get our answer to 43758 in its simplest radical form as follows:

√43758 = A√B

√43758 = 3√4862

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43758 to simplify the square root of 43758 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 43758 and then take the square root of that product. The prime factors that multiply together to make 43758 are 2 x 3 x 3 x 11 x 13 x 17. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 43758 by the number (A) squared. 3 squared is 9 and 43758 divided by 9 is 4862. Therefore, B equals 4862.

Once again we have A and B and can get our answer to 43758 in its simplest radical form as follows:

√43758 = A√B

√43758 = 3√4862

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