Hello! If you can help me with these 3 questions I would love it!
1. How do you simplify sqrt5 + 6 sqrt 5? I think that it is 5 sqrt10. Am I correct?
2. 5 sqrt 7 +2 sqrt 175. I think the answer is 7 sqrt 182
3. What is the domain of this function y = sqrt 3x+3. I really need help on this one.
Can someone just explain this too me? I don't want to just get the answers. I want to learn it. Thanks again!
The Great Undertale Fanatic
sqrt5 + 6 sqrt 5
= √5 + 6√5
= 1√5 + 6√5
1 apple + 6 apples = 7 apples
1 coffee + 6 coffees = 7 coffees
1x + 6x = 7x
1√5 + 6√5 = 7√5
You can easily verify this with your calculator
√5 = 2.236067977..
6√5 = 13.41640786..
so √5 + 6√5 = 2.236067977.. + 13.41640786.. = 15.65247584... (my calculator rounded)
7√5 = 15.65247584...
but your 5√10 answer would be 15.811388.. ≠ 7√5
for 5√7 +2√175
we cannot add them they way they sit, just like we couldn't add 5x + 2y
BUT ....
√175 = (√25)(√7) = 5√7 , we can only do this if one or more of the factors
are perfect squares.
5√7 +2√175
= 5√7 + 5√7
= 10√7 , (same as in our previous question).
again, check with your calculator
for y = √( 3x+3)
remember we cannot take the square root of a negative, so
3x+3 ≥ 0
divide both sides by +3, (nothing happens to the ≥ sign)
x + 3 ≥ 0
subtract 3 from both sides:
x ≥ -3 <------- your domain
Thank you for helping me on this!
You are welcome
Hello! I'll be happy to help you understand how to solve these questions.
1. To simplify sqrt5 + 6 sqrt 5, we can start by noticing that sqrt5 and 6 sqrt 5 have a common factor of sqrt5. We can factor this out:
sqrt5 + 6 sqrt 5 = sqrt5(1 + 6) = sqrt5 * 7 = 7 sqrt5
Therefore, the simplified form of sqrt5 + 6 sqrt 5 is 7 sqrt5.
Your answer of 5 sqrt10 is not correct because the expression given does not contain sqrt10.
2. To simplify 5 sqrt 7 + 2 sqrt 175, we can start by simplifying the expression under the square root symbols. sqrt 7 cannot be simplified further, but sqrt 175 can be broken down as follows:
sqrt 175 = sqrt (25 * 7) = sqrt 25 * sqrt 7 = 5 sqrt 7
Now we can substitute this value into the original expression:
5 sqrt 7 + 2 sqrt 175 = 5 sqrt 7 + 2 * 5 sqrt 7 = 5 sqrt 7 (1 + 2) = 5 sqrt 7 * 3 = 15 sqrt 7
So the correct answer is 15 sqrt 7, not 7 sqrt 182.
3. To find the domain of the function y = sqrt(3x + 3), we need to determine the set of valid inputs for x that will not result in undefined values or errors.
In this case, we need to consider the square root of a number. The square root is defined only for non-negative numbers, so the expression inside the square root (3x + 3) must be greater than or equal to zero:
3x + 3 ≥ 0
Solving this inequality:
3x ≥ -3
x ≥ -1
Therefore, the domain of the function is all real numbers greater than or equal to -1.
I hope this explanation helps you understand how to solve these questions! Let me know if you have any further questions.