Simplify Square Root of 45000

Here we will show you two methods that you can use to simplify the square root of 45000. In other words, we will show you how to find the square root of 45000 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.

√45000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45000 to simplify the square root of 45000. 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 45000. The factors of 45000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 625, 750, 900, 1000, 1125, 1250, 1500, 1800, 1875, 2250, 2500, 3000, 3750, 4500, 5000, 5625, 7500, 9000, 11250, 15000, 22500, and 45000. Furthermore, the greatest perfect square on this list is 22500 and the square root of 22500 is 150. Therefore, A equals 150.

B = Calculate 45000 divided by the greatest perfect square from the list of all factors of 45000. We determined above that the greatest perfect square from the list of all factors of 45000 is 22500. Furthermore, 45000 divided by 22500 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 45000 in its simplest radical form as follows:

√45000 = A√B

√45000 = 150√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45000 to simplify the square root of 45000 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 45000 and then take the square root of that product. The prime factors that multiply together to make 45000 are 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5 = 22500 and the square root of 22500 is 150. Therefore, A equals 150.

B = Divide 45000 by the number (A) squared. 150 squared is 22500 and 45000 divided by 22500 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 45000 in its simplest radical form as follows:

√45000 = A√B

√45000 = 150√2

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Simplify Square Root of 45001
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