Simplify Square Root of 59408

Here we will show you two methods that you can use to simplify the square root of 59408. In other words, we will show you how to find the square root of 59408 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.

√59408 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59408 to simplify the square root of 59408. 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 59408. The factors of 59408 are 1, 2, 4, 8, 16, 47, 79, 94, 158, 188, 316, 376, 632, 752, 1264, 3713, 7426, 14852, 29704, and 59408. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 59408 divided by the greatest perfect square from the list of all factors of 59408. We determined above that the greatest perfect square from the list of all factors of 59408 is 16. Furthermore, 59408 divided by 16 is 3713, therefore B equals 3713.

Now we have A and B and can get our answer to 59408 in its simplest radical form as follows:

√59408 = A√B

√59408 = 4√3713

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59408 to simplify the square root of 59408 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 59408 and then take the square root of that product. The prime factors that multiply together to make 59408 are 2 x 2 x 2 x 2 x 47 x 79. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 59408 by the number (A) squared. 4 squared is 16 and 59408 divided by 16 is 3713. Therefore, B equals 3713.

Once again we have A and B and can get our answer to 59408 in its simplest radical form as follows:

√59408 = A√B

√59408 = 4√3713

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Simplify Square Root of 59409
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