Simplify Square Root of 75810

Here we will show you two methods that you can use to simplify the square root of 75810. In other words, we will show you how to find the square root of 75810 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.

√75810 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75810 to simplify the square root of 75810. 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 75810. The factors of 75810 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 19, 21, 30, 35, 38, 42, 57, 70, 95, 105, 114, 133, 190, 210, 266, 285, 361, 399, 570, 665, 722, 798, 1083, 1330, 1805, 1995, 2166, 2527, 3610, 3990, 5054, 5415, 7581, 10830, 12635, 15162, 25270, 37905, and 75810. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 75810 divided by the greatest perfect square from the list of all factors of 75810. We determined above that the greatest perfect square from the list of all factors of 75810 is 361. Furthermore, 75810 divided by 361 is 210, therefore B equals 210.

Now we have A and B and can get our answer to 75810 in its simplest radical form as follows:

√75810 = A√B

√75810 = 19√210

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75810 to simplify the square root of 75810 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 75810 and then take the square root of that product. The prime factors that multiply together to make 75810 are 2 x 3 x 5 x 7 x 19 x 19. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 75810 by the number (A) squared. 19 squared is 361 and 75810 divided by 361 is 210. Therefore, B equals 210.

Once again we have A and B and can get our answer to 75810 in its simplest radical form as follows:

√75810 = A√B

√75810 = 19√210

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