Simplify Square Root of 42598

Here we will show you two methods that you can use to simplify the square root of 42598. In other words, we will show you how to find the square root of 42598 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.

√42598 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42598 to simplify the square root of 42598. 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 42598. The factors of 42598 are 1, 2, 19, 38, 59, 118, 361, 722, 1121, 2242, 21299, and 42598. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 42598 divided by the greatest perfect square from the list of all factors of 42598. We determined above that the greatest perfect square from the list of all factors of 42598 is 361. Furthermore, 42598 divided by 361 is 118, therefore B equals 118.

Now we have A and B and can get our answer to 42598 in its simplest radical form as follows:

√42598 = A√B

√42598 = 19√118

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42598 to simplify the square root of 42598 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 42598 and then take the square root of that product. The prime factors that multiply together to make 42598 are 2 x 19 x 19 x 59. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 42598 by the number (A) squared. 19 squared is 361 and 42598 divided by 361 is 118. Therefore, B equals 118.

Once again we have A and B and can get our answer to 42598 in its simplest radical form as follows:

√42598 = A√B

√42598 = 19√118

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Simplify Square Root of 42599
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