Simplify Square Root of 93969

Here we will show you two methods that you can use to simplify the square root of 93969. In other words, we will show you how to find the square root of 93969 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.

√93969 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93969 to simplify the square root of 93969. 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 93969. The factors of 93969 are 1, 3, 9, 53, 159, 197, 477, 591, 1773, 10441, 31323, and 93969. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 93969 divided by the greatest perfect square from the list of all factors of 93969. We determined above that the greatest perfect square from the list of all factors of 93969 is 9. Furthermore, 93969 divided by 9 is 10441, therefore B equals 10441.

Now we have A and B and can get our answer to 93969 in its simplest radical form as follows:

√93969 = A√B

√93969 = 3√10441

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93969 to simplify the square root of 93969 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 93969 and then take the square root of that product. The prime factors that multiply together to make 93969 are 3 x 3 x 53 x 197. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 93969 by the number (A) squared. 3 squared is 9 and 93969 divided by 9 is 10441. Therefore, B equals 10441.

Once again we have A and B and can get our answer to 93969 in its simplest radical form as follows:

√93969 = A√B

√93969 = 3√10441

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Simplify Square Root of 93970
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