Simplify Square Root of 43350

Here we will show you two methods that you can use to simplify the square root of 43350. In other words, we will show you how to find the square root of 43350 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.

√43350 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43350 to simplify the square root of 43350. 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 43350. The factors of 43350 are 1, 2, 3, 5, 6, 10, 15, 17, 25, 30, 34, 50, 51, 75, 85, 102, 150, 170, 255, 289, 425, 510, 578, 850, 867, 1275, 1445, 1734, 2550, 2890, 4335, 7225, 8670, 14450, 21675, and 43350. Furthermore, the greatest perfect square on this list is 7225 and the square root of 7225 is 85. Therefore, A equals 85.

B = Calculate 43350 divided by the greatest perfect square from the list of all factors of 43350. We determined above that the greatest perfect square from the list of all factors of 43350 is 7225. Furthermore, 43350 divided by 7225 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 43350 in its simplest radical form as follows:

√43350 = A√B

√43350 = 85√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43350 to simplify the square root of 43350 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 43350 and then take the square root of that product. The prime factors that multiply together to make 43350 are 2 x 3 x 5 x 5 x 17 x 17. When we strip out the pairs only, we get 5 x 5 x 17 x 17 = 7225 and the square root of 7225 is 85. Therefore, A equals 85.

B = Divide 43350 by the number (A) squared. 85 squared is 7225 and 43350 divided by 7225 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 43350 in its simplest radical form as follows:

√43350 = A√B

√43350 = 85√6

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 43351
Here is the next square root on our list that we have simplifed for you.