Question

find the real solution of the following radical equation.

(9sqrt{a} - 57 = 42)

(a = ?)

Explanation:

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<reasoning>

Isolate the radical term

\[

$$\begin{aligned} 9\sqrt{a} - 57 &= 42 \\ 9\sqrt{a} &= 42 + 57 \\ 9\sqrt{a} &= 99 \end{aligned}$$

\]

Divide by the coefficient

\[

$$\begin{aligned} \sqrt{a} &= \frac{99}{9} \\ \sqrt{a} &= 11 \end{aligned}$$

\]

Square both sides to solve for a

\[

$$\begin{aligned} a &= 11^2 \\ a &= 121 \end{aligned}$$

\]
</reasoning>

<answer>
Find the real solution of the following radical equation.

\(9\sqrt{a} - 57 = 42\)

\(a =\) <blank>121</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Radical Equations"
]
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</post_analysis>

Answer:

<pre_analysis>
{
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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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],
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],
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]
}
</pre_analysis>

<reasoning>

Isolate the radical term

\[

$$\begin{aligned} 9\sqrt{a} - 57 &= 42 \\ 9\sqrt{a} &= 42 + 57 \\ 9\sqrt{a} &= 99 \end{aligned}$$

\]

Divide by the coefficient

\[

$$\begin{aligned} \sqrt{a} &= \frac{99}{9} \\ \sqrt{a} &= 11 \end{aligned}$$

\]

Square both sides to solve for a

\[

$$\begin{aligned} a &= 11^2 \\ a &= 121 \end{aligned}$$

\]
</reasoning>

<answer>
Find the real solution of the following radical equation.

\(9\sqrt{a} - 57 = 42\)

\(a =\) <blank>121</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Radical Equations"
]
}
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