Question

question 6 (1 point) (03.01 mc) simplify 3√5 - 2√7 + √45 - √28. a 2√12 b 2√2 c 6√5 - 4√7 d 6√10 - 4√14 question 7 (1 point) (03.01 mc) simplify √5 • √8. a 2√10 b 4√10 c √40 d √13

Explanation:

Question 6

Step1: Simplify each square - root term

We know that $\sqrt{45}=\sqrt{9\times5} = 3\sqrt{5}$ and $\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}$.
The expression $3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}$ becomes $3\sqrt{5}-2\sqrt{7}+3\sqrt{5}-2\sqrt{7}$.

Step2: Combine like - terms

Combining the $\sqrt{5}$ terms: $3\sqrt{5}+3\sqrt{5}=6\sqrt{5}$.
Combining the $\sqrt{7}$ terms: $- 2\sqrt{7}-2\sqrt{7}=-4\sqrt{7}$.
So the simplified expression is $6\sqrt{5}-4\sqrt{7}$.

Step1: Use the property $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$

For $\sqrt{5}\cdot\sqrt{8}$, we have $\sqrt{5\times8}=\sqrt{40}$.
We can further simplify $\sqrt{40}$ as $\sqrt{4\times10}=2\sqrt{10}$ since $\sqrt{4\times10}=\sqrt{4}\cdot\sqrt{10}$ and $\sqrt{4} = 2$.

Answer:

$6\sqrt{5}-4\sqrt{7}$

Question 7