Grade HS Cla Rational numbers a $\newline$ Name: $\newline$ $1$ . Shade in the boxes of two numbers whose sum, when added, would be irrational. $\newline$ \begin{tabular}{|c|c|c|c|c|} $\newline$ \hline \begin{tabular}{c} $\newline$ ratival \\ $\newline$ $2 \sqrt{16}$ \\ $\newline$ $6$ $\newline$ \end{tabular} & \begin{tabular}{c} $\newline$ rationat \\ $\newline$ $2$ $\newline$ \end{tabular} & \begin{tabular}{c} $\newline$ $1$ \\ $\newline$ $5$ $\newline$ \end{tabular} & $\frac{4}{3}$ & $4 \sqrt{10}$ \\ $\newline$ \hline $\newline$ \end{tabular}

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Q. Grade HS Cla Rational numbers a

\newline

Name:

\newline

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 \begin{tabular}{c}

\newline

ratival \\

\newline

2 \sqrt{16}

\newline

6

\newline

\end{tabular} & \begin{tabular}{c}

\newline

rationat \\

\newline

2

\newline

\end{tabular} & \begin{tabular}{c}

\newline

1

\newline

5

\newline

\end{tabular} &

\frac{4}{3}

4 \sqrt{10}

\newline

\hline

\newline

\end{tabular}

Simplify square root of $16$ : The first number to consider is $2\sqrt{16}$ , which simplifies to $2\times 4$ because the square root of $16$ is $4$ . $\newline$ $2\sqrt{16} = 2\times 4 = 8$ $\newline$ This is a rational number because it can be expressed as a ratio of two integers.
Multiply by $4$ : The second number to consider is $4\sqrt{10}$ . Since the square root of $10$ is an irrational number, multiplying it by $4$ does not change its irrational nature. Therefore, $4\sqrt{10}$ is an irrational number.
Add rational and irrational numbers: To find a sum that is irrational, we can add a rational number to an irrational number. The sum of a rational and an irrational number is always irrational.
Find sum of numbers: Adding the rational number $8$ (from $2\sqrt{16}$ ) to the irrational number $4\sqrt{10}$ will give us an irrational sum. $\newline$ $8 + 4\sqrt{10} = 8 + 4\sqrt{10}$ $\newline$ This sum is irrational because it cannot be expressed as a ratio of two integers.