Simplify Square Root of 77616

Here we will show you two methods that you can use to simplify the square root of 77616. In other words, we will show you how to find the square root of 77616 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.

√77616 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77616 to simplify the square root of 77616. 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 77616. The factors of 77616 are 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 21, 22, 24, 28, 33, 36, 42, 44, 48, 49, 56, 63, 66, 72, 77, 84, 88, 98, 99, 112, 126, 132, 144, 147, 154, 168, 176, 196, 198, 231, 252, 264, 294, 308, 336, 392, 396, 441, 462, 504, 528, 539, 588, 616, 693, 784, 792, 882, 924, 1008, 1078, 1176, 1232, 1386, 1584, 1617, 1764, 1848, 2156, 2352, 2772, 3234, 3528, 3696, 4312, 4851, 5544, 6468, 7056, 8624, 9702, 11088, 12936, 19404, 25872, 38808, and 77616. Furthermore, the greatest perfect square on this list is 7056 and the square root of 7056 is 84. Therefore, A equals 84.

B = Calculate 77616 divided by the greatest perfect square from the list of all factors of 77616. We determined above that the greatest perfect square from the list of all factors of 77616 is 7056. Furthermore, 77616 divided by 7056 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 77616 in its simplest radical form as follows:

√77616 = A√B

√77616 = 84√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77616 to simplify the square root of 77616 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 77616 and then take the square root of that product. The prime factors that multiply together to make 77616 are 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7 = 7056 and the square root of 7056 is 84. Therefore, A equals 84.

B = Divide 77616 by the number (A) squared. 84 squared is 7056 and 77616 divided by 7056 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 77616 in its simplest radical form as follows:

√77616 = A√B

√77616 = 84√11

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Simplify Square Root of 77617
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