Rationalise (1 + √2)/(3 − 2√2) 🎥 Video Solution: 📘 Rationalise & Simplify: \[ \frac{1 + \sqrt{2}}{3 – 2\sqrt{2}} \] ✏️ Solution: \[ = \frac{1 + \sqrt{2}}{3 – 2\sqrt{2}} \times \frac{3 + 2\sqrt{2}}{3 + 2\sqrt{2}} \] \[ = \frac{(1 + \sqrt{2})(3 + 2\sqrt{2})}{3^2 – (2\sqrt{2})^2} \] \[ = \frac{3 + 2\sqrt{2} + 3\sqrt{2} + 4}{9 […]

Rationalise (5 + 2√3)/(7 + 4√3) 🎥 Video Solution: 📘 Rationalise & Simplify: \[ \frac{5 + 2\sqrt{3}}{7 + 4\sqrt{3}} \] ✏️ Solution: \[ = \frac{5 + 2\sqrt{3}}{7 + 4\sqrt{3}} \times \frac{7 – 4\sqrt{3}}{7 – 4\sqrt{3}} \] \[ = \frac{(5 + 2\sqrt{3})(7 – 4\sqrt{3})}{7^2 – (4\sqrt{3})^2} \] \[ = \frac{35 – 20\sqrt{3} + 14\sqrt{3} – 24}{49

Rationalise (2√6 − √5)/(3√5 − 2√6) 🎥 Video Solution: 📘 Rationalise & Simplify: \[ \frac{2\sqrt{6} – \sqrt{5}}{3\sqrt{5} – 2\sqrt{6}} \] ✏️ Solution: \[ = \frac{2\sqrt{6} – \sqrt{5}}{3\sqrt{5} – 2\sqrt{6}} \times \frac{3\sqrt{5} + 2\sqrt{6}}{3\sqrt{5} + 2\sqrt{6}} \] \[ = \frac{(2\sqrt{6} – \sqrt{5})(3\sqrt{5} + 2\sqrt{6})}{(3\sqrt{5})^2 – (2\sqrt{6})^2} \] \[ = \frac{6\sqrt{30} + 24 – 15 – 2\sqrt{30}}{45

Rationalise (2 + √3)/(2 − √3) 🎥 Video Solution: 📘 Rationalise: \[ \frac{2 + \sqrt{3}}{2 – \sqrt{3}} \] ✏️ Solution: \[ = \frac{2 + \sqrt{3}}{2 – \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} \] \[ = \frac{(2 + \sqrt{3})^2}{4 – 3} \] \[ = 4 + 3 + 4\sqrt{3} \] \[ = 7 + 4\sqrt{3}

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}