Question

Copy and complete the statement with <,>, or =.(Number 9 and 10)

Answer 1

The answer is:

`2(1)/(3)>2`

SOLUTION

Problem Statement

The question tells us to insert the right sign: "<, >, or =", given the following:

`\sqrt[]{(49)/(9)}_{}\text{ \_\_\_\_\_\_\_\_ 2}`

Method

To solve the question, we simply need to simplify the square root.

The law of indices we would use is given below:

`\sqrt[]{(a^2)/(b^2)}=(a)/(b)`

After this, we can easily compare the result from the above simplification and 2.

The meaning of the symbols being used here are:

`\begin{gathered} \text{'<' = Less than} \\ ^(\prime)>^(\prime)=\text{Greater than} \\ ^(\prime)=^(\prime)=\text{Equal to} \end{gathered}`

Thus, with this information, we can proceed to solve the question.

Implementation

`\begin{gathered} \sqrt[]{(49)/(9)}=\sqrt[]{(7^2)/(3^2)}=(7)/(3) \\ \\ (7)/(3)=2(1)/(3) \\ \\ \text{ Since }2(1)/(3)\text{ is }(1)/(3)\text{ greater than 2, thus, the correct expression is:} \\ \\ 2(1)/(3)>2 \end{gathered}`

The Final Answer is:

`2(1)/(3)>2`