Welp, my last post I wrote wrong and everyone was answering it wrong... my bad
Here are the questions:
(3√6 +5√10)^2
y = √6x-18
I couldn't figure out how to solve them, and I looked up online and here are the answers. I just need to be able to solve it...
286 + 60√15
x ≥ 3
By this time, you should have been able to find your answers in what was written in the responses.
Steve, I wrote the problems incorrectly, so no, I can't
Your text above seems to indicate that the last problem was to find the domain of √(6x-18)
You know that square roots of negative numbers are not real, so the radicand must be positive That is,
the domain of √x is x >= 0
So, the domain of √(6x-18) is
6x-18 >= 0
x >= 3
Look again for the answer to part 1. It is there.
No problem! I can help you understand how to solve the given problems. Let's take a look at each question and go through the steps to find the answer.
Question 1: (3√6 + 5√10)^2
To solve this problem, we will use the concept of expanding a binomial squared. Here's the step-by-step process:
1. Start with the expression: (3√6 + 5√10)^2.
2. Multiply the binomial by itself. This can be done using the FOIL method (First, Outer, Inner, Last) or by applying the distributive property twice.
(3√6 + 5√10)(3√6 + 5√10)
3. Use the distributive property to expand the expression:
(3√6)(3√6) + (3√6)(5√10) + (5√10)(3√6) + (5√10)(5√10)
4. Simplify each term:
9(√6)^2 + 15√6√10 + 15√6√10 + 25(√10)^2
5. Simplify each squared term:
9(6) + 15√60 + 15√60 + 25(10)
6. Further simplify the expressions inside the square roots:
54 + 15√60 + 15√60 + 250
7. Combine like terms:
54 + 30√60 + 250
8. Simplify the square root of 60:
54 + 30√(4 * 15) + 250
54 + 30(2√15) + 250
9. Multiply:
54 + 60√15 + 250
10. Combine like terms:
304 + 60√15
Therefore, the simplified answer is: 304 + 60√15.
Question 2: y = √6x - 18
To solve this equation for x, we'll follow these steps:
1. Start with the equation: y = √6x - 18.
2. Isolate the square root term by adding 18 to both sides of the equation:
y + 18 = √6x.
3. Square both sides of the equation to eliminate the square root:
(y + 18)^2 = (√6x)^2.
4. Simplify the equation:
y^2 + 36y + 18^2 = (√6)^2 * x.
y^2 + 36y + 324 = 6x.
5. Divide both sides of the equation by 6:
(1/6)(y^2 + 36y + 324) = x.
6. Simplify:
(1/6)y^2 + 6y + 54 = x.
The simplified answer is x ≥ (1/6)y^2 + 6y + 54.
I hope this helps you understand the solution process for these problems. If you have any further questions, feel free to ask!