Simplify Square Root of 75280

Here we will show you two methods that you can use to simplify the square root of 75280. In other words, we will show you how to find the square root of 75280 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.

√75280 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75280 to simplify the square root of 75280. 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 75280. The factors of 75280 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 941, 1882, 3764, 4705, 7528, 9410, 15056, 18820, 37640, and 75280. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 75280 divided by the greatest perfect square from the list of all factors of 75280. We determined above that the greatest perfect square from the list of all factors of 75280 is 16. Furthermore, 75280 divided by 16 is 4705, therefore B equals 4705.

Now we have A and B and can get our answer to 75280 in its simplest radical form as follows:

√75280 = A√B

√75280 = 4√4705

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75280 to simplify the square root of 75280 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 75280 and then take the square root of that product. The prime factors that multiply together to make 75280 are 2 x 2 x 2 x 2 x 5 x 941. 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 75280 by the number (A) squared. 4 squared is 16 and 75280 divided by 16 is 4705. Therefore, B equals 4705.

Once again we have A and B and can get our answer to 75280 in its simplest radical form as follows:

√75280 = A√B

√75280 = 4√4705

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Simplify Square Root of 75281
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