1. Simplify 2 over √5

Question

2. Simplify -11√112

3. Simplify 17√17-9√17

4. simplify 6 over √3 + 2

5. what is the domain of the function y=3√6x+42

6. What are the domain and range of the function y=2√3x+4-5

Answer 1

1. To simplify 2 over √5, we can rationalize the denominator by multiplying by √5/√5:
2/√5 * √5/√5 = 2√5/5

2. To simplify -11√112, we can first simplify the square root:
√112 = √16 * √7 = 4√7
Then we can substitute this back into the original expression:
-11 * 4√7 = -44√7

3. To simplify 17√17 - 9√17, we can combine the like terms:
(17-9)√17 = 8√17

4. To simplify 6 over √3 + 2, we can rationalize the denominator by multiplying by (√3 - 2)/(√3 - 2):
6/(√3 + 2) * (√3 - 2)/(√3 - 2) = (6√3 - 12)/(3 - 2√3)

5. The domain of the function y=3√6x+42 is all real numbers. There are no restrictions on x that would make the square root negative or undefined.

6. The domain of the function y=2√3x+4-5 is all real numbers. The range, however, is bounded below by -5, as the smallest value the function can output is when x = 0, yielding y = -5. The function can take on any value greater than or equal to -5.

Answer 2

#4 , wrong answer by the bot
6/ (√3 + 2)
= 6/ (√3 + 2) * (√3 - 2)/(√3 - 2)
= (6√3 - 12)/(3 - 4)
= 12 - 6√3

#5 careful when you write something like y=3√6x+42
the way you typed it , it means y= (3√6)x + 42
and the bot is right by saying the domain is the set of real numbers
but...
perhaps you meant y=3√(6x+42), then the domain would be
6x + 42 > 0 , which means x > -7

#6, same situation as #5
because of the unusual 4 - 5 at then end, my guess would be that you mean
y=2√(3x+4) - 5

In that case the domain is
x > -4/3

Answer 3

You are correct, thank you for catching those errors. My apologies for any confusion caused. Your solutions for #4, #5, and #6 are all correct.