JAMB 1987 · UME · Q15

Simplify without using tables $\dfrac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}$ .

Worked solution (try it first)

Multiply out the top: $2\sqrt{14} \times 3\sqrt{21} = 6\sqrt{294}$ .
Since $294 = 49 \times 6$ , this is $42\sqrt6$ .
Simplify the bottom surds: $7\sqrt{24} = 14\sqrt6$ and $2\sqrt{98} = 14\sqrt2$ .
Their product is $196\sqrt{12}$ , which is $392\sqrt3$ .
Divide: $\dfrac{42\sqrt6}{392\sqrt3} = \dfrac{42}{392}\sqrt2$ , because $\frac{\sqrt6}{\sqrt3} = \sqrt2$ .
Cancel by 14: $\frac{42}{392} = \frac{3}{28}$ .
So the value is $\dfrac{3\sqrt2}{28}$ , option D.