Simplify Square Root of 9522

Here we will show you two methods that you can use to simplify the square root of 9522. In other words, we will show you how to find the square root of 9522 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.

√9522 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9522 to simplify the square root of 9522. 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 9522. The factors of 9522 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414, 529, 1058, 1587, 3174, 4761, and 9522. Furthermore, the greatest perfect square on this list is 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Calculate 9522 divided by the greatest perfect square from the list of all factors of 9522. We determined above that the greatest perfect square from the list of all factors of 9522 is 4761. Furthermore, 9522 divided by 4761 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 9522 in its simplest radical form as follows:

√9522 = A√B

√9522 = 69√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9522 to simplify the square root of 9522 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 9522 and then take the square root of that product. The prime factors that multiply together to make 9522 are 2 x 3 x 3 x 23 x 23. When we strip out the pairs only, we get 3 x 3 x 23 x 23 = 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Divide 9522 by the number (A) squared. 69 squared is 4761 and 9522 divided by 4761 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 9522 in its simplest radical form as follows:

√9522 = A√B

√9522 = 69√2

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Simplify Square Root of 9523
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