Question

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

Answer 1

Answer

The answer is:

$2\frac{1}{3}>2$

SOLUTION

Problem Statement

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

$\sqrt[]{\frac{49}{9}}_{}\text{ \_\_\_\_\_\_\_\_ 2}$

Method

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

The law of indices we would use is given below:

$\sqrt[]{\frac{a^2}{b^2}}=\frac{a}{b}$

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

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

The Final Answer is:

$2\frac{1}{3}>2$