Discussion

If \(9\sqrt{x} = \sqrt{12} + \sqrt{147}\) then x =?

Answer: B

The value of x is 3.

Simplify each root by taking out square factors:

\[ \begin{aligned} \sqrt{12} + \sqrt{147} &= 2\sqrt{3} + 7\sqrt{3} \\ &= 9\sqrt{3} \end{aligned} \]

So \(9\sqrt{x} = 9\sqrt{3}\) and \(x = 3\). Adding the numbers under the roots (12 + 147 = 159) is the common error and gives none of the options.

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