Evaluate sqrt7x (sqrt x-7 sqrt7) Show your work.
sqrt(7)*sqrt(x)-sqrt(7)*7*sqrt(7)
sqrt(7*x)-7*sqrt(7*7)
sqrt(7x)-7*sqrt(7^2)
x*sqrt 7x-49*x
^^^ would this be my final answer?
Assuming you meant:
√7 x(√x - 7√7)
= x√(7x) - 49x
brackets are important here
e.g √(7x) vs √7x , the last one is (√7)x
To evaluate the expression sqrt(7x)(sqrt(x)-7sqrt(7)), let's break it down step by step:
1. Distribute sqrt(7x) to both terms inside the parentheses:
sqrt(7x) * sqrt(x) - sqrt(7x) * 7 * sqrt(7)
2. Simplify each term:
sqrt(7 * x^2) - 7 * sqrt(7^2)
3. Simplify the square root:
sqrt(7x^2) - 7 * sqrt(49)
4. Simplify the square roots of 7 and 49:
x * sqrt(7x) - 7 * 7
5. Simplify sqrt(7x) as the final answer:
x * sqrt(7x) - 49
Therefore, the final answer is x * sqrt(7x) - 49.
No, your final answer is not correct. Let's evaluate the expression step by step:
Given expression: sqrt(7x) * (sqrt(x) - 7 * sqrt(7))
Using the distributive property, we can simplify this expression:
sqrt(7x) * sqrt(x) - 7 * sqrt(7x) * sqrt(7)
Now, simplify each term separately:
1) sqrt(7x) * sqrt(x)
= sqrt(7x^2) (using the product rule of square roots)
= sqrt(7) * sqrt(x^2) (splitting the square root)
= sqrt(7) * x (since sqrt(x^2) = x)
2) - 7 * sqrt(7x) * sqrt(7)
= -7 * sqrt(7x * 7) (combining inside the square root)
= -7 * sqrt(49x)
= -7 * 7 * sqrt(x) (splitting the square root)
= -49sqrt(x)
Now combine the simplified terms:
sqrt(7x) * sqrt(x) - 7 * sqrt(7x) * sqrt(7)
= sqrt(7) * x - 49sqrt(x)
So the correct final answer is sqrt(7)x - 49sqrt(x).