Simplify Square Root of 34322

Here we will show you two methods that you can use to simplify the square root of 34322. In other words, we will show you how to find the square root of 34322 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.

√34322 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34322 to simplify the square root of 34322. 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 34322. The factors of 34322 are 1, 2, 131, 262, 17161, and 34322. Furthermore, the greatest perfect square on this list is 17161 and the square root of 17161 is 131. Therefore, A equals 131.

B = Calculate 34322 divided by the greatest perfect square from the list of all factors of 34322. We determined above that the greatest perfect square from the list of all factors of 34322 is 17161. Furthermore, 34322 divided by 17161 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 34322 in its simplest radical form as follows:

√34322 = A√B

√34322 = 131√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34322 to simplify the square root of 34322 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 34322 and then take the square root of that product. The prime factors that multiply together to make 34322 are 2 x 131 x 131. When we strip out the pairs only, we get 131 x 131 = 17161 and the square root of 17161 is 131. Therefore, A equals 131.

B = Divide 34322 by the number (A) squared. 131 squared is 17161 and 34322 divided by 17161 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 34322 in its simplest radical form as follows:

√34322 = A√B

√34322 = 131√2

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Simplify Square Root of 34323
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