Simplify Square Root of 42354

Here we will show you two methods that you can use to simplify the square root of 42354. In other words, we will show you how to find the square root of 42354 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.

√42354 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42354 to simplify the square root of 42354. 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 42354. The factors of 42354 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 181, 234, 362, 543, 1086, 1629, 2353, 3258, 4706, 7059, 14118, 21177, and 42354. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 42354 divided by the greatest perfect square from the list of all factors of 42354. We determined above that the greatest perfect square from the list of all factors of 42354 is 9. Furthermore, 42354 divided by 9 is 4706, therefore B equals 4706.

Now we have A and B and can get our answer to 42354 in its simplest radical form as follows:

√42354 = A√B

√42354 = 3√4706

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42354 to simplify the square root of 42354 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 42354 and then take the square root of that product. The prime factors that multiply together to make 42354 are 2 x 3 x 3 x 13 x 181. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 42354 by the number (A) squared. 3 squared is 9 and 42354 divided by 9 is 4706. Therefore, B equals 4706.

Once again we have A and B and can get our answer to 42354 in its simplest radical form as follows:

√42354 = A√B

√42354 = 3√4706

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Simplify Square Root of 42355
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