Simplify Square Root of 83300

Here we will show you two methods that you can use to simplify the square root of 83300. In other words, we will show you how to find the square root of 83300 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.

√83300 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83300 to simplify the square root of 83300. 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 83300. The factors of 83300 are 1, 2, 4, 5, 7, 10, 14, 17, 20, 25, 28, 34, 35, 49, 50, 68, 70, 85, 98, 100, 119, 140, 170, 175, 196, 238, 245, 340, 350, 425, 476, 490, 595, 700, 833, 850, 980, 1190, 1225, 1666, 1700, 2380, 2450, 2975, 3332, 4165, 4900, 5950, 8330, 11900, 16660, 20825, 41650, and 83300. Furthermore, the greatest perfect square on this list is 4900 and the square root of 4900 is 70. Therefore, A equals 70.

B = Calculate 83300 divided by the greatest perfect square from the list of all factors of 83300. We determined above that the greatest perfect square from the list of all factors of 83300 is 4900. Furthermore, 83300 divided by 4900 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 83300 in its simplest radical form as follows:

√83300 = A√B

√83300 = 70√17

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83300 to simplify the square root of 83300 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 83300 and then take the square root of that product. The prime factors that multiply together to make 83300 are 2 x 2 x 5 x 5 x 7 x 7 x 17. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 7 x 7 = 4900 and the square root of 4900 is 70. Therefore, A equals 70.

B = Divide 83300 by the number (A) squared. 70 squared is 4900 and 83300 divided by 4900 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 83300 in its simplest radical form as follows:

√83300 = A√B

√83300 = 70√17

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Simplify Square Root of 83301
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