Question

15. Pat and Camilla are working with expressions with rational exponents. Listed below are what eachbelieves to be correct. Use the properties of exponents to determine the correct answer. Writethe correct answer in the space provided.

Answer 1

√2 +√8=3 (2 ^1/2)

1) Solving this expression we have

`\begin{gathered} \sqrt[]{2}\text{ +}\sqrt[]{8}= \\ \sqrt[]{2}\text{ +2}\sqrt[]{2} \end{gathered}`

2) Since we can rewrite this expression using the exponents like this

`\begin{gathered} 2^{(1)/(2)}+2(2^{(1)/(2)})\cong4.24 \\ 3(2^{(1)/(2)})\cong4.24 \end{gathered}`

and since 2 raised to 1/2 works like a term, we can add. Just like we do to

x + 2x = 3x.

So the answer is √2 +√8=3 (2 ^1/2) =

√