Simplify Square Root of 42238

Here we will show you two methods that you can use to simplify the square root of 42238. In other words, we will show you how to find the square root of 42238 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.

√42238 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42238 to simplify the square root of 42238. 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 42238. The factors of 42238 are 1, 2, 7, 14, 49, 98, 431, 862, 3017, 6034, 21119, and 42238. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 42238 divided by the greatest perfect square from the list of all factors of 42238. We determined above that the greatest perfect square from the list of all factors of 42238 is 49. Furthermore, 42238 divided by 49 is 862, therefore B equals 862.

Now we have A and B and can get our answer to 42238 in its simplest radical form as follows:

√42238 = A√B

√42238 = 7√862

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42238 to simplify the square root of 42238 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 42238 and then take the square root of that product. The prime factors that multiply together to make 42238 are 2 x 7 x 7 x 431. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 42238 by the number (A) squared. 7 squared is 49 and 42238 divided by 49 is 862. Therefore, B equals 862.

Once again we have A and B and can get our answer to 42238 in its simplest radical form as follows:

√42238 = A√B

√42238 = 7√862

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Simplify Square Root of 42239
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