Simplify Square Root of 29768

Here we will show you two methods that you can use to simplify the square root of 29768. In other words, we will show you how to find the square root of 29768 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.

√29768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 29768 to simplify the square root of 29768. 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 29768. The factors of 29768 are 1, 2, 4, 8, 61, 122, 244, 488, 3721, 7442, 14884, and 29768. Furthermore, the greatest perfect square on this list is 14884 and the square root of 14884 is 122. Therefore, A equals 122.

B = Calculate 29768 divided by the greatest perfect square from the list of all factors of 29768. We determined above that the greatest perfect square from the list of all factors of 29768 is 14884. Furthermore, 29768 divided by 14884 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 29768 in its simplest radical form as follows:

√29768 = A√B

√29768 = 122√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 29768 to simplify the square root of 29768 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 29768 and then take the square root of that product. The prime factors that multiply together to make 29768 are 2 x 2 x 2 x 61 x 61. When we strip out the pairs only, we get 2 x 2 x 61 x 61 = 14884 and the square root of 14884 is 122. Therefore, A equals 122.

B = Divide 29768 by the number (A) squared. 122 squared is 14884 and 29768 divided by 14884 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 29768 in its simplest radical form as follows:

√29768 = A√B

√29768 = 122√2

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Simplify Square Root of 29769
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