Simplify Square Root of 42608

Here we will show you two methods that you can use to simplify the square root of 42608. In other words, we will show you how to find the square root of 42608 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.

√42608 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42608 to simplify the square root of 42608. 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 42608. The factors of 42608 are 1, 2, 4, 8, 16, 2663, 5326, 10652, 21304, and 42608. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 42608 divided by the greatest perfect square from the list of all factors of 42608. We determined above that the greatest perfect square from the list of all factors of 42608 is 16. Furthermore, 42608 divided by 16 is 2663, therefore B equals 2663.

Now we have A and B and can get our answer to 42608 in its simplest radical form as follows:

√42608 = A√B

√42608 = 4√2663

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42608 to simplify the square root of 42608 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 42608 and then take the square root of that product. The prime factors that multiply together to make 42608 are 2 x 2 x 2 x 2 x 2663. 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 42608 by the number (A) squared. 4 squared is 16 and 42608 divided by 16 is 2663. Therefore, B equals 2663.

Once again we have A and B and can get our answer to 42608 in its simplest radical form as follows:

√42608 = A√B

√42608 = 4√2663

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Simplify Square Root of 42609
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