$1$ . Shade in the boxes of two numbers whose sum, when added, would be irrational. $\newline$ \begin{tabular}{|c|c|c|c|c|} $\newline$ \hline raturs & & Irrdt & $4^{r^{d}}$ & त्रण \\ $\newline$ \hline $2 \sqrt{16}$ & & $\sqrt{5}$ & $\frac{4}{3}$ & $4 \sqrt{10}$ \\ $\newline$ \hline $\newline$ \end{tabular}

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Algebra 2

Find trigonometric ratios using reference angles

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1

. Shade in the boxes of two numbers whose sum, when added, would be irrational.

\newline

\begin{tabular}{|c|c|c|c|c|}

\newline

\hline raturs & & Irrdt &

4^{r^{d}}

& त्रण \\

\newline

\hline

2 \sqrt{16}

& &

\sqrt{5}

\frac{4}{3}

4 \sqrt{10}

\newline

\hline

\newline

\end{tabular}

Understand Numbers: Understand the nature of the numbers given. $\newline$ We need to identify two numbers from the list that, when added together, will result in an irrational number. An irrational number is a number that cannot be expressed as a simple fraction, meaning its decimal form goes on forever without repeating. Rational numbers, on the other hand, can be expressed as fractions of integers.
Evaluate Types: Evaluate each number to determine if it is rational or irrational. $\newline$ - ＂raturs＂ and ＂Irrdt＂ are not recognizable mathematical terms or numbers, so we cannot use them. $\newline$ - ＂ $4^{(r^{d})}$ ＂ seems to be an expression with unspecified variables $r$ and $d$ , so we cannot determine if it is rational or irrational without additional information. $\newline$ - ＂त्रण＂ is a word in Devanagari script and does not represent a number. $\newline$ - ＂ $2\sqrt{16}$ ＂ simplifies to $2 \times 4 = 8$ , which is a rational number. $\newline$ - ＂ $\sqrt{5}$ ＂ is an irrational number because the square root of $5$ cannot be expressed as a fraction of two integers. $\newline$ - ＂ $(4)/(3)$ ＂ is a fraction, which is a rational number. $\newline$ - ＂ $4\sqrt{10}$ ＂ is an irrational number because the square root of $10$ is irrational, and multiplying it by $4$ does not change that.
Select Irrational Numbers: Select two numbers from the list that are irrational. $\newline$ From our evaluation in Step $2$ , the two irrational numbers we can identify are $\sqrt{5}$ and $4\sqrt{10}$ .
Add Irrational Numbers: Add the two irrational numbers together to ensure their sum is also irrational. $\newline$ The sum of $\sqrt{5}$ and $4\sqrt{10}$ is $\sqrt{5} + 4\sqrt{10}$ . Since both terms involve square roots of non-perfect squares, their sum is also irrational.