Simplify Square Root of 176

Here we will show you two methods that you can use to simplify the square root of 176. In other words, we will show you how to find the square root of 176 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.

√176 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 176 to simplify the square root of 176. 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 176. The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 176 divided by the greatest perfect square from the list of all factors of 176. We determined above that the greatest perfect square from the list of all factors of 176 is 16. Furthermore, 176 divided by 16 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 176 in its simplest radical form as follows:

√176 = A√B

√176 = 4√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 176 to simplify the square root of 176 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 176 and then take the square root of that product. The prime factors that multiply together to make 176 are 2 x 2 x 2 x 2 x 11. 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 176 by the number (A) squared. 4 squared is 16 and 176 divided by 16 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 176 in its simplest radical form as follows:

√176 = A√B

√176 = 4√11

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Simplify Square Root of 177
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