Simplify Square Root of 4590

Here we will show you two methods that you can use to simplify the square root of 4590. In other words, we will show you how to find the square root of 4590 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.

√4590 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 4590 to simplify the square root of 4590. 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 4590. The factors of 4590 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 27, 30, 34, 45, 51, 54, 85, 90, 102, 135, 153, 170, 255, 270, 306, 459, 510, 765, 918, 1530, 2295, and 4590. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 4590 divided by the greatest perfect square from the list of all factors of 4590. We determined above that the greatest perfect square from the list of all factors of 4590 is 9. Furthermore, 4590 divided by 9 is 510, therefore B equals 510.

Now we have A and B and can get our answer to 4590 in its simplest radical form as follows:

√4590 = A√B

√4590 = 3√510

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 4590 to simplify the square root of 4590 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 4590 and then take the square root of that product. The prime factors that multiply together to make 4590 are 2 x 3 x 3 x 3 x 5 x 17. 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 4590 by the number (A) squared. 3 squared is 9 and 4590 divided by 9 is 510. Therefore, B equals 510.

Once again we have A and B and can get our answer to 4590 in its simplest radical form as follows:

√4590 = A√B

√4590 = 3√510

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