WAEC Mathematics 2023 Paper

Concept:Simplify the surds by removing perfect square factors and rationalizing the denominator before combining like terms.Explanation:Start with the expression $3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}.$Observe that $12 = 4 \times 3$, so $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$.Therefore, $3\sqrt{12} = 3 \times 2\sqrt{3} = 6\sqrt{3}$.Substitute this back into the expression:$6\sqrt{3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}.$Rationalize the fraction: $\frac{6}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$.Now the expression becomes $6\sqrt{3} + 10\sqrt{3} - 2\sqrt{3}$.All terms are like surds, so combine their coefficients:$(6 + 10 - 2)\sqrt{3} = 14\sqrt{3}.$Thus, the simplified form is $14\sqrt{3}$.Answer:$14\sqrt{3}$Option C.