Question

Zoe and Marsden are working with expressions with rational exponents. Zoe believes V2+ V8 is equivalent to 2.21. Marsden believes v2 + V8 is equivalent to 3.21. Use the properties of exponents to decide who is correct. Write the correct answer in the space provided.

Answer 1

Step-by-step explanation

the properties of exponents

`\begin{gathered} \sqrt[n]{a}=a^{(1)/(n)} \\ \sqrt[n]{a^{n^{}}b^n}\text{ = ab} \\ \sqrt[]{ab}=\sqrt[]{a}\cdot\sqrt[]{b} \end{gathered}`

Step 1

Zoe believes

`\sqrt[]{2}+\sqrt[]{8\text{ }}=\text{ 2.21}`

Marsden Believes

`\sqrt[]{2}+\sqrt[]{8}=3.21`

Step 2

`\sqrt[]{8}=\sqrt[]{4}\cdot\sqrt[]{2}=\text{ 2}\sqrt[]{2}`

then

`\begin{gathered} \sqrt[]{2}+\sqrt[]{8}=\text{ }\sqrt[]{2}+2\sqrt[]{2}=3\sqrt[]{2} \\ \text{also } \\ \sqrt[]{2}=\text{ 1.4142} \\ so, \\ \sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24 \end{gathered}`

then

`\sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24`

I hope this helps you