Simplify Square Root of 84388

Here we will show you two methods that you can use to simplify the square root of 84388. In other words, we will show you how to find the square root of 84388 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.

√84388 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84388 to simplify the square root of 84388. 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 84388. The factors of 84388 are 1, 2, 4, 17, 34, 68, 73, 146, 289, 292, 578, 1156, 1241, 2482, 4964, 21097, 42194, and 84388. Furthermore, the greatest perfect square on this list is 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Calculate 84388 divided by the greatest perfect square from the list of all factors of 84388. We determined above that the greatest perfect square from the list of all factors of 84388 is 1156. Furthermore, 84388 divided by 1156 is 73, therefore B equals 73.

Now we have A and B and can get our answer to 84388 in its simplest radical form as follows:

√84388 = A√B

√84388 = 34√73

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84388 to simplify the square root of 84388 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 84388 and then take the square root of that product. The prime factors that multiply together to make 84388 are 2 x 2 x 17 x 17 x 73. When we strip out the pairs only, we get 2 x 2 x 17 x 17 = 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Divide 84388 by the number (A) squared. 34 squared is 1156 and 84388 divided by 1156 is 73. Therefore, B equals 73.

Once again we have A and B and can get our answer to 84388 in its simplest radical form as follows:

√84388 = A√B

√84388 = 34√73

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Simplify Square Root of 84389
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