Simplify Square Root of 46240

Here we will show you two methods that you can use to simplify the square root of 46240. In other words, we will show you how to find the square root of 46240 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.

√46240 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 46240 to simplify the square root of 46240. 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 46240. The factors of 46240 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 68, 80, 85, 136, 160, 170, 272, 289, 340, 544, 578, 680, 1156, 1360, 1445, 2312, 2720, 2890, 4624, 5780, 9248, 11560, 23120, and 46240. Furthermore, the greatest perfect square on this list is 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Calculate 46240 divided by the greatest perfect square from the list of all factors of 46240. We determined above that the greatest perfect square from the list of all factors of 46240 is 4624. Furthermore, 46240 divided by 4624 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 46240 in its simplest radical form as follows:

√46240 = A√B

√46240 = 68√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 46240 to simplify the square root of 46240 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 46240 and then take the square root of that product. The prime factors that multiply together to make 46240 are 2 x 2 x 2 x 2 x 2 x 5 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 17 x 17 = 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Divide 46240 by the number (A) squared. 68 squared is 4624 and 46240 divided by 4624 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 46240 in its simplest radical form as follows:

√46240 = A√B

√46240 = 68√10

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