Simplify Square Root of 70227

Here we will show you two methods that you can use to simplify the square root of 70227. In other words, we will show you how to find the square root of 70227 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.

√70227 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70227 to simplify the square root of 70227. 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 70227. The factors of 70227 are 1, 3, 9, 17, 27, 51, 81, 153, 243, 289, 459, 867, 1377, 2601, 4131, 7803, 23409, and 70227. Furthermore, the greatest perfect square on this list is 23409 and the square root of 23409 is 153. Therefore, A equals 153.

B = Calculate 70227 divided by the greatest perfect square from the list of all factors of 70227. We determined above that the greatest perfect square from the list of all factors of 70227 is 23409. Furthermore, 70227 divided by 23409 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 70227 in its simplest radical form as follows:

√70227 = A√B

√70227 = 153√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70227 to simplify the square root of 70227 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 70227 and then take the square root of that product. The prime factors that multiply together to make 70227 are 3 x 3 x 3 x 3 x 3 x 17 x 17. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 17 x 17 = 23409 and the square root of 23409 is 153. Therefore, A equals 153.

B = Divide 70227 by the number (A) squared. 153 squared is 23409 and 70227 divided by 23409 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 70227 in its simplest radical form as follows:

√70227 = A√B

√70227 = 153√3

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Simplify Square Root of 70228
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