Simplify Square Root of 73776

Here we will show you two methods that you can use to simplify the square root of 73776. In other words, we will show you how to find the square root of 73776 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.

√73776 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73776 to simplify the square root of 73776. 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 73776. The factors of 73776 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 53, 58, 87, 106, 116, 159, 174, 212, 232, 318, 348, 424, 464, 636, 696, 848, 1272, 1392, 1537, 2544, 3074, 4611, 6148, 9222, 12296, 18444, 24592, 36888, and 73776. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 73776 divided by the greatest perfect square from the list of all factors of 73776. We determined above that the greatest perfect square from the list of all factors of 73776 is 16. Furthermore, 73776 divided by 16 is 4611, therefore B equals 4611.

Now we have A and B and can get our answer to 73776 in its simplest radical form as follows:

√73776 = A√B

√73776 = 4√4611

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73776 to simplify the square root of 73776 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 73776 and then take the square root of that product. The prime factors that multiply together to make 73776 are 2 x 2 x 2 x 2 x 3 x 29 x 53. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 73776 by the number (A) squared. 4 squared is 16 and 73776 divided by 16 is 4611. Therefore, B equals 4611.

Once again we have A and B and can get our answer to 73776 in its simplest radical form as follows:

√73776 = A√B

√73776 = 4√4611

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Simplify Square Root of 73777
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