Simplify Square Root of 43550

Here we will show you two methods that you can use to simplify the square root of 43550. In other words, we will show you how to find the square root of 43550 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.

√43550 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43550 to simplify the square root of 43550. 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 43550. The factors of 43550 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 67, 130, 134, 325, 335, 650, 670, 871, 1675, 1742, 3350, 4355, 8710, 21775, and 43550. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 43550 divided by the greatest perfect square from the list of all factors of 43550. We determined above that the greatest perfect square from the list of all factors of 43550 is 25. Furthermore, 43550 divided by 25 is 1742, therefore B equals 1742.

Now we have A and B and can get our answer to 43550 in its simplest radical form as follows:

√43550 = A√B

√43550 = 5√1742

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43550 to simplify the square root of 43550 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 43550 and then take the square root of that product. The prime factors that multiply together to make 43550 are 2 x 5 x 5 x 13 x 67. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 43550 by the number (A) squared. 5 squared is 25 and 43550 divided by 25 is 1742. Therefore, B equals 1742.

Once again we have A and B and can get our answer to 43550 in its simplest radical form as follows:

√43550 = A√B

√43550 = 5√1742

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Simplify Square Root of 43551
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