May 2026

Rationalise (3√2 + 1)/(2√5 − 3) 🎥 Video Solution: 📘 Rationalise: \[ \frac{3\sqrt{2} + 1}{2\sqrt{5} – 3} \] ✏️ Solution: \[ = \frac{3\sqrt{2} + 1}{2\sqrt{5} – 3} \times \frac{2\sqrt{5} + 3}{2\sqrt{5} + 3} \] \[ = \frac{(3\sqrt{2} + 1)(2\sqrt{5} + 3)}{(2\sqrt{5})^2 – 3^2} \] \[ = \frac{6\sqrt{10} + 9\sqrt{2} + 2\sqrt{5} + 3}{20 – 9} […]

Rationalise √b²/(√(a² + √b²) + a) 🎥 Video Solution: 📘 Rationalise: \[ \frac{\sqrt{b^2}}{\sqrt{a^2 + \sqrt{b^2}} + a} \] ✏️ Solution: \[ \sqrt{b^2} = b \] \[ = \frac{b}{\sqrt{a^2 + b} + a} \] \[ \times \frac{\sqrt{a^2 + b} – a}{\sqrt{a^2 + b} – a} \] \[ = \frac{b(\sqrt{a^2 + b} – a)}{(a^2 + b) –

Rationalise (6 − 4√2)/(6 + 4√2) 🎥 Video Solution: 📘 Rationalise: \[ \frac{6 – 4\sqrt{2}}{6 + 4\sqrt{2}} \] ✏️ Solution: \[ = \frac{6 – 4\sqrt{2}}{6 + 4\sqrt{2}} \times \frac{6 – 4\sqrt{2}}{6 – 4\sqrt{2}} \] \[ = \frac{(6 – 4\sqrt{2})^2}{6^2 – (4\sqrt{2})^2} \] \[ = \frac{36 + 32 – 48\sqrt{2}}{36 – 32} \] \[ = \frac{68

Rationalise (√3 + 1)/(2√2 − √3) 🎥 Video Solution: 📘 Rationalise: \[ \frac{\sqrt{3} + 1}{2\sqrt{2} – \sqrt{3}} \] ✏️ Solution: \[ = \frac{\sqrt{3} + 1}{2\sqrt{2} – \sqrt{3}} \times \frac{2\sqrt{2} + \sqrt{3}}{2\sqrt{2} + \sqrt{3}} \] \[ = \frac{(\sqrt{3} + 1)(2\sqrt{2} + \sqrt{3})}{(2\sqrt{2})^2 – (\sqrt{3})^2} \] \[ = \frac{2\sqrt{6} + 3 + 2\sqrt{2} + \sqrt{3}}{8 – 3}

Rationalise 1/(2√5 − √3) 🎥 Video Solution: 📘 Rationalise: \[ \frac{1}{2\sqrt{5} – \sqrt{3}} \] ✏️ Solution: \[ = \frac{1}{2\sqrt{5} – \sqrt{3}} \times \frac{2\sqrt{5} + \sqrt{3}}{2\sqrt{5} + \sqrt{3}} \] \[ = \frac{2\sqrt{5} + \sqrt{3}}{(2\sqrt{5})^2 – (\sqrt{3})^2} \] \[ = \frac{2\sqrt{5} + \sqrt{3}}{20 – 3} \] \[ = \frac{2\sqrt{5} + \sqrt{3}}{17} \] ✅ Final Answer: \(\frac{2\sqrt{5} +

Rationalise 30/(5√3 − 3√5) 🎥 Video Solution: 📘 Rationalise: \[ \frac{30}{5\sqrt{3} – 3\sqrt{5}} \] ✏️ Solution: \[ = \frac{30}{5\sqrt{3} – 3\sqrt{5}} \times \frac{5\sqrt{3} + 3\sqrt{5}}{5\sqrt{3} + 3\sqrt{5}} \] \[ = \frac{30(5\sqrt{3} + 3\sqrt{5})}{(5\sqrt{3})^2 – (3\sqrt{5})^2} \] \[ = \frac{30(5\sqrt{3} + 3\sqrt{5})}{75 – 45} \] \[ = \frac{30(5\sqrt{3} + 3\sqrt{5})}{30} \] \[ = 5\sqrt{3} + 3\sqrt{5}

Rationalise 16/(√41 − 5) 🎥 Video Solution: 📘 Rationalise: \[ \frac{16}{\sqrt{41} – 5} \] ✏️ Solution: \[ = \frac{16}{\sqrt{41} – 5} \times \frac{\sqrt{41} + 5}{\sqrt{41} + 5} \] \[ = \frac{16(\sqrt{41} + 5)}{41 – 25} \] \[ = \frac{16(\sqrt{41} + 5)}{16} \] \[ = \sqrt{41} + 5 \] ✅ Final Answer: \(\sqrt{41} + 5\) Next

Rationalise 1/(√6 − √5) 🎥 Video Solution: 📘 Rationalise: \[ \frac{1}{\sqrt{6} – \sqrt{5}} \] ✏️ Solution: \[ = \frac{1}{\sqrt{6} – \sqrt{5}} \times \frac{\sqrt{6} + \sqrt{5}}{\sqrt{6} + \sqrt{5}} \] \[ = \frac{\sqrt{6} + \sqrt{5}}{6 – 5} \] \[ = \sqrt{6} + \sqrt{5} \] ✅ Final Answer: \(\sqrt{6} + \sqrt{5}\) Next Question / Full Exercise

Rationalise √6/(√2 + √3) 🎥 Video Solution: 📘 Rationalise: \[ \frac{\sqrt{6}}{\sqrt{2} + \sqrt{3}} \] ✏️ Solution: \[ = \frac{\sqrt{6}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} – \sqrt{3}}{\sqrt{2} – \sqrt{3}} \] \[ = \frac{\sqrt{6}(\sqrt{2} – \sqrt{3})}{2 – 3} \] \[ = \frac{\sqrt{12} – \sqrt{18}}{-1} \] \[ = \frac{2\sqrt{3} – 3\sqrt{2}}{-1} \] \[ = 3\sqrt{2} – 2\sqrt{3} \] ✅

Find value of surds expressions 🎥 Video Solution: 📘 Find the values: 1. \[ \frac{2 + \sqrt{3}}{3} \] \[ = \frac{2 + 1.732}{3} \] \[ = \frac{3.732}{3} \] \[ = 1.244 \] ✅ Answer: \(1.244\) 2. \[ \frac{\sqrt{2} – 1}{\sqrt{5}} \] \[ = \frac{1.414 – 1}{2.236} \] \[ = \frac{0.414}{2.236} \] \[ \approx 0.185 \]