Question

find the value of x and y. state your solution in simplest radical form where \\(x = a\sqrt{b}\\) and \\(y = c\sqrt{d}\\), where a and c are coefficients and b and d are radicands. use na when necessary.

\\(a = \\)
\\(b = \\)
\\(c = \\)
\\(d = \\)

Explanation:

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<reasoning>

Find the value of x

\[

$$\begin{aligned} &x = 6\sqrt{2} \end{aligned}$$

\]

Find the value of y

\[

$$\begin{aligned} &y = (6\sqrt{2}) \cdot \sqrt{2} = 6 \cdot 2 = 12 \end{aligned}$$

\]

Determine the coefficients and radicands

\[

$$\begin{aligned} &x = a\sqrt{b} \implies 6\sqrt{2} \implies a = 6,\ b = 2\\ &y = c\sqrt{d} \implies 12 \implies 12\sqrt{1} \implies c = 12,\ d = 1 \end{aligned}$$

\]
</reasoning>

<answer>
Find the value of x and y. State your solution in simplest radical form where \(x = a\sqrt{b}\) and \(y = c\sqrt{d}\), where a and c are coefficients and b and d are radicands. Use NA when necessary.

\(a =\) <blank>6</blank>
\(b =\) <blank>2</blank>
\(c =\) <blank>12</blank>
\(d =\) <blank>1</blank>
</answer>

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"Special Right Triangles"
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Answer:

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<reasoning>

Find the value of x

\[

$$\begin{aligned} &x = 6\sqrt{2} \end{aligned}$$

\]

Find the value of y

\[

$$\begin{aligned} &y = (6\sqrt{2}) \cdot \sqrt{2} = 6 \cdot 2 = 12 \end{aligned}$$

\]

Determine the coefficients and radicands

\[

$$\begin{aligned} &x = a\sqrt{b} \implies 6\sqrt{2} \implies a = 6,\ b = 2\\ &y = c\sqrt{d} \implies 12 \implies 12\sqrt{1} \implies c = 12,\ d = 1 \end{aligned}$$

\]
</reasoning>

<answer>
Find the value of x and y. State your solution in simplest radical form where \(x = a\sqrt{b}\) and \(y = c\sqrt{d}\), where a and c are coefficients and b and d are radicands. Use NA when necessary.

\(a =\) <blank>6</blank>
\(b =\) <blank>2</blank>
\(c =\) <blank>12</blank>
\(d =\) <blank>1</blank>
</answer>

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"Mathematics",
"Geometry",
"Special Right Triangles"
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