Simplify Square Root of 9350

Here we will show you two methods that you can use to simplify the square root of 9350. In other words, we will show you how to find the square root of 9350 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.

√9350 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9350 to simplify the square root of 9350. 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 9350. The factors of 9350 are 1, 2, 5, 10, 11, 17, 22, 25, 34, 50, 55, 85, 110, 170, 187, 275, 374, 425, 550, 850, 935, 1870, 4675, and 9350. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 9350 divided by the greatest perfect square from the list of all factors of 9350. We determined above that the greatest perfect square from the list of all factors of 9350 is 25. Furthermore, 9350 divided by 25 is 374, therefore B equals 374.

Now we have A and B and can get our answer to 9350 in its simplest radical form as follows:

√9350 = A√B

√9350 = 5√374

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9350 to simplify the square root of 9350 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 9350 and then take the square root of that product. The prime factors that multiply together to make 9350 are 2 x 5 x 5 x 11 x 17. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 9350 by the number (A) squared. 5 squared is 25 and 9350 divided by 25 is 374. Therefore, B equals 374.

Once again we have A and B and can get our answer to 9350 in its simplest radical form as follows:

√9350 = A√B

√9350 = 5√374

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Simplify Square Root of 9351
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