Simplify Square Root of 74350

Here we will show you two methods that you can use to simplify the square root of 74350. In other words, we will show you how to find the square root of 74350 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.

√74350 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74350 to simplify the square root of 74350. 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 74350. The factors of 74350 are 1, 2, 5, 10, 25, 50, 1487, 2974, 7435, 14870, 37175, and 74350. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 74350 divided by the greatest perfect square from the list of all factors of 74350. We determined above that the greatest perfect square from the list of all factors of 74350 is 25. Furthermore, 74350 divided by 25 is 2974, therefore B equals 2974.

Now we have A and B and can get our answer to 74350 in its simplest radical form as follows:

√74350 = A√B

√74350 = 5√2974

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74350 to simplify the square root of 74350 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 74350 and then take the square root of that product. The prime factors that multiply together to make 74350 are 2 x 5 x 5 x 1487. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 74350 by the number (A) squared. 5 squared is 25 and 74350 divided by 25 is 2974. Therefore, B equals 2974.

Once again we have A and B and can get our answer to 74350 in its simplest radical form as follows:

√74350 = A√B

√74350 = 5√2974

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Simplify Square Root of 74351
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