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Real Numbers — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsReal Numbers2 Marks
Question
Multiply : $(3 \sqrt{2}-\sqrt{3})(4 \sqrt{3}-\sqrt{2})$
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Answer

$\begin{aligned} & (3 \sqrt{2}-\sqrt{3})(4 \sqrt{3}-\sqrt{2}) \\ = & 3 \sqrt{2}(4 \sqrt{3}-\sqrt{2})-\sqrt{3}(4 \sqrt{3}-\sqrt{2}) \\ = & 3 \sqrt{2} \times 4 \sqrt{3}-3 \sqrt{2} \times \sqrt{2} \\ & \quad-\sqrt{3} \times 4 \sqrt{3}+\sqrt{3} \times \sqrt{2} \\ = & 12 \sqrt{2 \times 3}-3 \sqrt{2 \times 2}-4 \sqrt{3 \times 3}+\sqrt{3 \times 2} \\ = & 12 \sqrt{6}-(3 \times 2)-(4 \times 3)+\sqrt{6} \\ = & 12 \sqrt{6}-6-12+\sqrt{6} \\ = & (12+1) \sqrt{6}-6-12 \\ = & 13 \sqrt{6}-18 \\ \therefore \quad & (3 \sqrt{2}-\sqrt{3})(4 \sqrt{3}-\sqrt{2})=13 \sqrt{6}-18\end{aligned}$

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