Question

Operations with Radical Expressions I’m still learning about this concept and I’m having trouble understanding the complexity of the problem!

Answer 1

Answer:

Explanation:

Question 3.

Before we simplify the radical expression let us note the following.

$\begin{gathered} 27=9\times3 \\ 45=9\times5 \end{gathered}$

Therefore, we can write our radical function as

$\begin{gathered} -\sqrt[]{27}-2\sqrt[]{27}+2\sqrt[]{45} \\ \Rightarrow-\sqrt[]{9\times3}-2\sqrt[]{9\times3}+2\sqrt[]{9\times5} \end{gathered}$

Now,

$\begin{gathered} \sqrt[]{9\times3}=\sqrt[]{9}\times\sqrt[]{3}=3\sqrt[]{3} \\ \sqrt[]{9\times5}=\sqrt[]{9}\times\sqrt[]{5}=3\sqrt[]{5} \end{gathered}$

therefore, our expression becomes

$\begin{gathered} -\sqrt[]{9\times3}-2\sqrt[]{9\times3}+2\sqrt[]{9\times5} \\ \Rightarrow-3\sqrt[]{3}-2(3\sqrt[]{3})+2(3\sqrt[]{5}) \end{gathered}$

which simplifies to give

$-3\sqrt[]{3}-6\sqrt[]{3}+6\sqrt[]{5}$

since -3√3 - 6 √3 = - 9 √3 ( just add them up), the above becomes

$-9\sqrt[]{3}+6\sqrt[]{5}$

We cannot simplify the above function any further. Therefore, the above expression is our final answer.

Question 5.

Since -3√ 27 - 3√27 = -6 √27, our expression becomes

$-3\sqrt[]{20}-6\sqrt[]{27}$

Let us also note that

$\begin{gathered} 20=4\times5 \\ 27=3\times9 \end{gathered}$

therefore,

$\begin{gathered} \sqrt[]{27}=\sqrt[]{3\times9} \\ \sqrt[]{20}=\sqrt[]{4\times5} \end{gathered}$

therefore, our expression becomes

$-3\sqrt[]{4\times5}-6\sqrt[]{3\times9}$

Now since

$\begin{gathered} \sqrt[]{4\times5}=\sqrt[]{4}\times\sqrt[]{5}=2\sqrt[]{5} \\ \sqrt[]{3\times9}=\sqrt[]{3}\times\sqrt[]{9}=3\sqrt[]{3} \end{gathered}$

the above becomes

$-3(2\sqrt[]{5})-6(3\sqrt[]{3})$$\Rightarrow-6\sqrt[]{5}-18\sqrt[]{3}$

We cannot simplify the above function any further. Therefore, the above expression is our final answer.