Simplify Square Root of 69776

Here we will show you two methods that you can use to simplify the square root of 69776. In other words, we will show you how to find the square root of 69776 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.

√69776 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69776 to simplify the square root of 69776. 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 69776. The factors of 69776 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 89, 98, 112, 178, 196, 356, 392, 623, 712, 784, 1246, 1424, 2492, 4361, 4984, 8722, 9968, 17444, 34888, and 69776. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 69776 divided by the greatest perfect square from the list of all factors of 69776. We determined above that the greatest perfect square from the list of all factors of 69776 is 784. Furthermore, 69776 divided by 784 is 89, therefore B equals 89.

Now we have A and B and can get our answer to 69776 in its simplest radical form as follows:

√69776 = A√B

√69776 = 28√89

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69776 to simplify the square root of 69776 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 69776 and then take the square root of that product. The prime factors that multiply together to make 69776 are 2 x 2 x 2 x 2 x 7 x 7 x 89. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 69776 by the number (A) squared. 28 squared is 784 and 69776 divided by 784 is 89. Therefore, B equals 89.

Once again we have A and B and can get our answer to 69776 in its simplest radical form as follows:

√69776 = A√B

√69776 = 28√89

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