how do you simplify square root of 27 minus square root of 49 all divided by square root of 3. I have gotten two different answers when I tried to check it. It kind of looks like (27-49)

(3)
except all the numbers have their own square root symbol. I don't know if it will be lined up when I post the question

do you mean

(√27 - √49)/√3 ??

if so then
= (3√3 - 7)/ 2√3

now if you want to rationalize that, multiply top and bottom by √3 to get

(9 - 7√3)/3

Where did you get the 2 from in the second part of your solution?

To simplify the given expression, square roots can be simplified individually and then the division can be performed.

Let's simplify each square root step-by-step:
1. Square root of 27 = sqrt(9) * sqrt(3) = 3 * sqrt(3)
2. Square root of 49 = sqrt(7) * sqrt(7) = 7

Now we can substitute these values back into the expression:

(sqrt(27) - sqrt(49)) / sqrt(3) = (3 * sqrt(3) - 7) / sqrt(3)

Since there is a common denominator, sqrt(3), we can combine the terms by multiplying both the numerator and the denominator by sqrt(3):

(3 * sqrt(3) - 7) / sqrt(3) * sqrt(3) / sqrt(3) = (3 * sqrt(3) - 7 * sqrt(3)) / (sqrt(3) * sqrt(3))
= (3 * sqrt(3) - 7 * sqrt(3)) / 3

Now, simplify the numerator:

= (3 - 7) * sqrt(3) / 3
= -4 * sqrt(3) / 3

So, the simplified expression is -4 * sqrt(3) / 3.

If you got a different answer, there might have been an error during the simplification process. Please recheck your work or provide your steps for further assistance.