Here we will show you two methods that you can use to simplify the square root of 33000. In other words, we will show you how to find the square root of 33000 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.

√33000 = A√B

**Greatest Perfect Square Factor Method**

The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33000 to simplify the square root of 33000. 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 33000. The factors of 33000 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 40, 44, 50, 55, 60, 66, 75, 88, 100, 110, 120, 125, 132, 150, 165, 200, 220, 250, 264, 275, 300, 330, 375, 440, 500, 550, 600, 660, 750, 825, 1000, 1100, 1320, 1375, 1500, 1650, 2200, 2750, 3000, 3300, 4125, 5500, 6600, 8250, 11000, 16500, and 33000. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

**B**= Calculate 33000 divided by the greatest perfect square from the list of all factors of 33000. We determined above that the greatest perfect square from the list of all factors of 33000 is 100. Furthermore, 33000 divided by 100 is 330, therefore B equals 330.

Now we have A and B and can get our answer to 33000 in its simplest radical form as follows:

√33000 = A√B

**√33000 = 10√330**

**Double Prime Factor Method**

The Double Prime Factor Method uses the prime factors of 33000 to simplify the square root of 33000 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 33000 and then take the square root of that product. The prime factors that multiply together to make 33000 are 2 x 2 x 2 x 3 x 5 x 5 x 5 x 11. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

**B**= Divide 33000 by the number (A) squared. 10 squared is 100 and 33000 divided by 100 is 330. Therefore, B equals 330.

Once again we have A and B and can get our answer to 33000 in its simplest radical form as follows:

√33000 = A√B

**√33000 = 10√330**

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