Educational

Simplify (11 + √11)(11 − √11) 🎥 Video Solution: 📘 Simplify: \[ (11 + \sqrt{11})(11 – \sqrt{11}) \] ✏️ Solution: \[ = 11^2 – (\sqrt{11})^2 \] \[ = 121 – 11 \] \[ = 110 \] ✅ Final Answer: \(110\) Next Question / Full Exercise

Simplify (√5 − 2)(√3 − √5) 🎥 Video Solution: 📘 Simplify: \[ (\sqrt{5} – 2)(\sqrt{3} – \sqrt{5}) \] ✏️ Solution: \[ = \sqrt{5}\sqrt{3} – \sqrt{5}\sqrt{5} – 2\sqrt{3} + 2\sqrt{5} \] \[ = \sqrt{15} – 5 – 2\sqrt{3} + 2\sqrt{5} \] ✅ Final Answer: \(\sqrt{15} – 2\sqrt{3} + 2\sqrt{5} – 5\) Next Question / Full Exercise

Simplify (3 + √3)(5 − √2) 🎥 Video Solution: 📘 Simplify: \[ (3 + \sqrt{3})(5 – \sqrt{2}) \] ✏️ Solution: \[ = 3\cdot5 – 3\sqrt{2} + 5\sqrt{3} – \sqrt{3}\sqrt{2} \] \[ = 15 – 3\sqrt{2} + 5\sqrt{3} – \sqrt{6} \] ✅ Final Answer: \(15 – 3\sqrt{2} + 5\sqrt{3} – \sqrt{6}\) Next Question / Full Exercise

Simplify (4 + √7)(3 + √2) 🎥 Video Solution: 📘 Simplify: \[ (4 + \sqrt{7})(3 + \sqrt{2}) \] ✏️ Solution: \[ = 4 \cdot 3 + 4\sqrt{2} + 3\sqrt{7} + \sqrt{7}\sqrt{2} \] \[ = 12 + 4\sqrt{2} + 3\sqrt{7} + \sqrt{14} \] ✅ Final Answer: \(12 + 4\sqrt{2} + 3\sqrt{7} + \sqrt{14}\) Next Question /

Simplify 4√28 ÷ 3√7 🎥 Video Solution: 📘 Simplify: \[ \frac{4\sqrt{28}}{3\sqrt{7}} \] ✏️ Solution: \[ = \frac{4}{3} \times \sqrt{\frac{28}{7}} \] \[ = \frac{4}{3} \times \sqrt{4} \] \[ = \frac{4}{3} \times 2 \] \[ = \frac{8}{3} \] ✅ Final Answer: \(\frac{8}{3}\) Next Question / Full Exercise

Simplify ⁴√1250 ÷ ⁴√2 🎥 Video Solution: 📘 Simplify: \[ \frac{\sqrt[4]{1250}}{\sqrt[4]{2}} \] ✏️ Solution: \[ \frac{\sqrt[4]{1250}}{\sqrt[4]{2}} = \sqrt[4]{\frac{1250}{2}} \] \[ = \sqrt[4]{625} \] \[ = \sqrt[4]{5^4} \] \[ = 5 \] ✅ Final Answer: \(5\) Next Question / Full Exercise

Simplify ∛4 × ∛16 🎥 Video Solution: 📘 Simplify: \[ \sqrt[3]{4} \times \sqrt[3]{16} \] ✏️ Solution: \[ \sqrt[3]{4} \times \sqrt[3]{16} = \sqrt[3]{4 \times 16} \] \[ = \sqrt[3]{64} \] \[ = 4 \] ✅ Final Answer: \(4\) Next Question / Full Exercise

Assertion Reason Exponents 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \left(\sqrt[m]{\sqrt[n]{a}}\right)^{mn} = a \) Statement-2: \( ((a^m)^n)^p = a^{mnp} \) ✏️ Solution \( \sqrt[n]{a} = a^{1/n} \) \( \sqrt[m]{\sqrt[n]{a}} = (a^{1/n})^{1/m} = a^{1/(mn)} \) \( \left(a^{1/(mn)}\right)^{mn} = a \) So Statement-1 is TRUE Statement-2 is also TRUE (law of exponents) Statement-2 correctly

Assertion Reason Infinite Roots 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} = 3 \) Statement-2: \( \sqrt{x+\sqrt{x+\sqrt{x+\cdots}}} = x,\ x>0 \) ✏️ Solution Let \( y = \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} \) Then \( y = \sqrt{6+y} \) Squaring: \( y^2 = 6 + y \) \( y^2 – y – 6 = 0

Assertion Reason Infinite Roots 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \sqrt{5\sqrt{5\sqrt{5\cdots}}} = 5\sqrt{5} \) Statement-2: \( \sqrt{x\sqrt{x\sqrt{x\cdots}}} = x,\ x>0 \) ✏️ Solution Let \( y = \sqrt{5\sqrt{5\sqrt{5\cdots}}} \) Then \( y = \sqrt{5y} \) Squaring: \( y^2 = 5y \) \( y(y-5) = 0 \Rightarrow y = 5 \) (since