Simplify Square Root of 162

Here we will show you two methods that you can use to simplify the square root of 162. In other words, we will show you how to find the square root of 162 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.

√162 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 162 to simplify the square root of 162. 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 162. The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 162 divided by the greatest perfect square from the list of all factors of 162. We determined above that the greatest perfect square from the list of all factors of 162 is 81. Furthermore, 162 divided by 81 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 162 in its simplest radical form as follows:

√162 = A√B

√162 = 9√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 162 to simplify the square root of 162 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 162 and then take the square root of that product. The prime factors that multiply together to make 162 are 2 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 162 by the number (A) squared. 9 squared is 81 and 162 divided by 81 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 162 in its simplest radical form as follows:

√162 = A√B

√162 = 9√2

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Simplify Square Root of 163
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