Simplify Square Root of 42000

Here we will show you two methods that you can use to simplify the square root of 42000. In other words, we will show you how to find the square root of 42000 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.

√42000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42000 to simplify the square root of 42000. 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 42000. The factors of 42000 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000, and 42000. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 42000 divided by the greatest perfect square from the list of all factors of 42000. We determined above that the greatest perfect square from the list of all factors of 42000 is 400. Furthermore, 42000 divided by 400 is 105, therefore B equals 105.

Now we have A and B and can get our answer to 42000 in its simplest radical form as follows:

√42000 = A√B

√42000 = 20√105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42000 to simplify the square root of 42000 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 42000 and then take the square root of that product. The prime factors that multiply together to make 42000 are 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 42000 by the number (A) squared. 20 squared is 400 and 42000 divided by 400 is 105. Therefore, B equals 105.

Once again we have A and B and can get our answer to 42000 in its simplest radical form as follows:

√42000 = A√B

√42000 = 20√105

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Simplify Square Root of 42001
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