Simplify Square Root of 76500

Here we will show you two methods that you can use to simplify the square root of 76500. In other words, we will show you how to find the square root of 76500 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.

√76500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 76500 to simplify the square root of 76500. 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 76500. The factors of 76500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 30, 34, 36, 45, 50, 51, 60, 68, 75, 85, 90, 100, 102, 125, 150, 153, 170, 180, 204, 225, 250, 255, 300, 306, 340, 375, 425, 450, 500, 510, 612, 750, 765, 850, 900, 1020, 1125, 1275, 1500, 1530, 1700, 2125, 2250, 2550, 3060, 3825, 4250, 4500, 5100, 6375, 7650, 8500, 12750, 15300, 19125, 25500, 38250, and 76500. Furthermore, the greatest perfect square on this list is 900 and the square root of 900 is 30. Therefore, A equals 30.

B = Calculate 76500 divided by the greatest perfect square from the list of all factors of 76500. We determined above that the greatest perfect square from the list of all factors of 76500 is 900. Furthermore, 76500 divided by 900 is 85, therefore B equals 85.

Now we have A and B and can get our answer to 76500 in its simplest radical form as follows:

√76500 = A√B

√76500 = 30√85

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 76500 to simplify the square root of 76500 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 76500 and then take the square root of that product. The prime factors that multiply together to make 76500 are 2 x 2 x 3 x 3 x 5 x 5 x 5 x 17. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 5 x 5 = 900 and the square root of 900 is 30. Therefore, A equals 30.

B = Divide 76500 by the number (A) squared. 30 squared is 900 and 76500 divided by 900 is 85. Therefore, B equals 85.

Once again we have A and B and can get our answer to 76500 in its simplest radical form as follows:

√76500 = A√B

√76500 = 30√85

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Simplify Square Root of 76501
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