Simplify Square Root of 74385

Here we will show you two methods that you can use to simplify the square root of 74385. In other words, we will show you how to find the square root of 74385 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.

√74385 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74385 to simplify the square root of 74385. 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 74385. The factors of 74385 are 1, 3, 5, 9, 15, 19, 27, 29, 45, 57, 87, 95, 135, 145, 171, 261, 285, 435, 513, 551, 783, 855, 1305, 1653, 2565, 2755, 3915, 4959, 8265, 14877, 24795, and 74385. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 74385 divided by the greatest perfect square from the list of all factors of 74385. We determined above that the greatest perfect square from the list of all factors of 74385 is 9. Furthermore, 74385 divided by 9 is 8265, therefore B equals 8265.

Now we have A and B and can get our answer to 74385 in its simplest radical form as follows:

√74385 = A√B

√74385 = 3√8265

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74385 to simplify the square root of 74385 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 74385 and then take the square root of that product. The prime factors that multiply together to make 74385 are 3 x 3 x 3 x 5 x 19 x 29. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 74385 by the number (A) squared. 3 squared is 9 and 74385 divided by 9 is 8265. Therefore, B equals 8265.

Once again we have A and B and can get our answer to 74385 in its simplest radical form as follows:

√74385 = A√B

√74385 = 3√8265

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Simplify Square Root of 74386
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