Simplify Square Root of 71383

Here we will show you two methods that you can use to simplify the square root of 71383. In other words, we will show you how to find the square root of 71383 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.

√71383 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71383 to simplify the square root of 71383. 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 71383. The factors of 71383 are 1, 13, 17, 19, 221, 247, 289, 323, 3757, 4199, 5491, and 71383. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 71383 divided by the greatest perfect square from the list of all factors of 71383. We determined above that the greatest perfect square from the list of all factors of 71383 is 289. Furthermore, 71383 divided by 289 is 247, therefore B equals 247.

Now we have A and B and can get our answer to 71383 in its simplest radical form as follows:

√71383 = A√B

√71383 = 17√247

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71383 to simplify the square root of 71383 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 71383 and then take the square root of that product. The prime factors that multiply together to make 71383 are 13 x 17 x 17 x 19. 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 71383 by the number (A) squared. 17 squared is 289 and 71383 divided by 289 is 247. Therefore, B equals 247.

Once again we have A and B and can get our answer to 71383 in its simplest radical form as follows:

√71383 = A√B

√71383 = 17√247

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Simplify Square Root of 71384
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