Simplify Square Root of 42160

Here we will show you two methods that you can use to simplify the square root of 42160. In other words, we will show you how to find the square root of 42160 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.

√42160 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42160 to simplify the square root of 42160. 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 42160. The factors of 42160 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 31, 34, 40, 62, 68, 80, 85, 124, 136, 155, 170, 248, 272, 310, 340, 496, 527, 620, 680, 1054, 1240, 1360, 2108, 2480, 2635, 4216, 5270, 8432, 10540, 21080, and 42160. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 42160 divided by the greatest perfect square from the list of all factors of 42160. We determined above that the greatest perfect square from the list of all factors of 42160 is 16. Furthermore, 42160 divided by 16 is 2635, therefore B equals 2635.

Now we have A and B and can get our answer to 42160 in its simplest radical form as follows:

√42160 = A√B

√42160 = 4√2635

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42160 to simplify the square root of 42160 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 42160 and then take the square root of that product. The prime factors that multiply together to make 42160 are 2 x 2 x 2 x 2 x 5 x 17 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 42160 by the number (A) squared. 4 squared is 16 and 42160 divided by 16 is 2635. Therefore, B equals 2635.

Once again we have A and B and can get our answer to 42160 in its simplest radical form as follows:

√42160 = A√B

√42160 = 4√2635

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