Simplify Square Root of 67383

Here we will show you two methods that you can use to simplify the square root of 67383. In other words, we will show you how to find the square root of 67383 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.

√67383 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 67383 to simplify the square root of 67383. 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 67383. The factors of 67383 are 1, 3, 9, 7487, 22461, and 67383. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 67383 divided by the greatest perfect square from the list of all factors of 67383. We determined above that the greatest perfect square from the list of all factors of 67383 is 9. Furthermore, 67383 divided by 9 is 7487, therefore B equals 7487.

Now we have A and B and can get our answer to 67383 in its simplest radical form as follows:

√67383 = A√B

√67383 = 3√7487

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 67383 to simplify the square root of 67383 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 67383 and then take the square root of that product. The prime factors that multiply together to make 67383 are 3 x 3 x 7487. 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 67383 by the number (A) squared. 3 squared is 9 and 67383 divided by 9 is 7487. Therefore, B equals 7487.

Once again we have A and B and can get our answer to 67383 in its simplest radical form as follows:

√67383 = A√B

√67383 = 3√7487

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Simplify Square Root of 67384
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