Mathematics 2014 JAMB Past Questions - Question 8: simplify 2√2 - √3 / √2 + √3

Correct Answer

B

Explanation

To simplify the expression \(\frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}}\), we can use the technique of rationalizing the denominator.First, we multiply both the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{2} - \sqrt{3}\):\(\frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)Expanding the numerator and the denominator, we get:\(\frac{(2\sqrt{2} - \sqrt{3})(\sqrt{2} - \sqrt{3})}{(\sqrt{2} + \sqrt{3})(\sqrt{2} - \sqrt{3})}\)Simplifying the numerator and the denominator, we get:\(\frac{2 \times 2 - 2\sqrt{6} - 3}{2 - 3}\)\(\frac{4 - 2\sqrt{6} - 3}{-1}\)\(\frac{1 - 2\sqrt{6}}{-1}\)Finally, multiplying the numerator and the denominator by -1, we get:\(-1 + 2\sqrt{6}\)So, the simplified form of the expression \(\frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}}\) is \(-1 + 2\sqrt{6}\).