Simplify Square Root of 34391

Here we will show you two methods that you can use to simplify the square root of 34391. In other words, we will show you how to find the square root of 34391 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.

√34391 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34391 to simplify the square root of 34391. 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 34391. The factors of 34391 are 1, 7, 17, 119, 289, 2023, 4913, and 34391. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 34391 divided by the greatest perfect square from the list of all factors of 34391. We determined above that the greatest perfect square from the list of all factors of 34391 is 289. Furthermore, 34391 divided by 289 is 119, therefore B equals 119.

Now we have A and B and can get our answer to 34391 in its simplest radical form as follows:

√34391 = A√B

√34391 = 17√119

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34391 to simplify the square root of 34391 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 34391 and then take the square root of that product. The prime factors that multiply together to make 34391 are 7 x 17 x 17 x 17. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 34391 by the number (A) squared. 17 squared is 289 and 34391 divided by 289 is 119. Therefore, B equals 119.

Once again we have A and B and can get our answer to 34391 in its simplest radical form as follows:

√34391 = A√B

√34391 = 17√119

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Simplify Square Root of 34392
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