Here is a list of solutions from Algebra chapter form Vedanta Excel in Mathematics Book 10: Exercise 8.1 - HCF Exercise 8.2 - LCM Exercise 9.1 - Simplification of Rational Expressions Exercise 10.1 - Simplification of Indices …

Question: Rationalize the denominators and simplify: $\dfrac{\sqrt{a+b} - \sqrt{a-b}}{\sqrt{a+b} + \sqrt{a-b}}$ Solution: Given, $= \dfrac{\sqrt{a+b} - \sqrt{a-b}}{\sqrt{a+b} + \sqrt{a-b}}$ $= \dfrac{\sqrt{a+b} - \sqrt{a-b}}{\sqrt{a+b} + \sqrt{a-b}} × \dfrac{\sqrt{a+b} - \sqrt{a-b}}{\sqrt{a+b} - \sqrt{a-b}}$ $= \dfrac{(\sqrt{a+b} …

Question: Rationalize the denominators and simplify: $\dfrac{2√3 - 3√2}{2√3 + 3√2}$ Solution: Given, $= \dfrac{2√3 - 3√2}{2√3 + 3√2}$ $= \dfrac{2√3 - 3√2}{2√3 + 3√2} × \dfrac{2√3 - 3√2}{2√3 - 3√2}$ $= \dfrac{(2√3-3√2)²}{(2√3)² - (3√2)²}$ $= \dfrac{(2√3)² - 2×2√3×3√2 + (3√2)²}{4×3 - 9×2}$ $= \dfrac{4×3 - 12√6 + 9×2}{12 - 18}$ $= \dfr…

Question: Rationalize the denominators and simplify: $\dfrac{√3 -√2}{√3+√2}$ Solution: Given, $= \dfrac{√3-√2}{√3+√2}$ $= \dfrac{√3-√2}{√3+√2} × \dfrac{√3-√2}{√3-√2}$ $= \dfrac{(√3-√2)²}{(√3)²-(√2)²}$ $= \dfrac{(√3)²-2×√3×√2 + (√3)²}{3-2}$ $= \dfrac{3 - 2√6 +2}{1}$ $= 5 - 2√6$ = Answer

Question: Rationalize the denominators and simplify: $\dfrac{√2 +1}{√2 -1}$ Solution: Given, $= \dfrac{√2 +1}{√2 -1}$ $= \dfrac{√2 +1}{√2-1} × \dfrac{√2+1}{√2+1}$ $= \dfrac{(√2+1)²}{(√2)²-(1)²}$ $= \dfrac{(√2)² + 2×√2×1 + 1²}{2-1}$ $= \dfrac{2+2√2 +1}{1}$ $= 3 +2√2$ = Answer

Question: Rationalize the denominators and simplify: $\dfrac{5√3}{2√3 - √2}$ Solution: Given, $= \dfrac{5√3}{2√3 - √2}$ $= \dfrac{5√3}{2√3 - √2} × \dfrac{2√3 + √2}{2√3 + √2}$ $= \dfrac{5√3 (2√3 +√2)}{(2√3)^2 - (√2)^2}$ $= \dfrac{5×2×\sqrt{3×3} + 5×\sqrt{2×3})}{12 - 2}$ $= \dfrac{10×3 + 5√6}{10}$ $= \dfrac{30 + 5√6}{10}$ $= \dfrac{5(…

Question: Rationalize the denominators and simplify: $\dfrac{5}{3\sqrt{7} + 2\sqrt{3}}$ Solution: Given, $= \dfrac{5}{3\sqrt{7} + 2\sqrt{3}}$ $= \dfrac{5}{3\sqrt{7} + 2\sqrt{3}} × \dfrac{3\sqrt{7} - 2\sqrt{3}}{3\sqrt{7} - 2\sqrt{3}}$ $= \dfrac{5(3\sqrt{7} - 2\sqrt{3})}{(3\sqrt{7})^2 - (2\sqrt{3})^2}$ $= \dfrac{5(3\sqrt{7} - 2\sqrt{3…

Question: Rationalize the denominators and simplify: $\dfrac{3}{\sqrt{5} - \sqrt{2}}$ Solution: Given, $= \dfrac{3}{\sqrt{5} - \sqrt{2}}$ $= \dfrac{3}{\sqrt{5} - \sqrt{2}} × \dfrac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$ $= \dfrac{3(\sqrt{5} + \sqrt{2}}{(\sqrt{5})^2 - (\sqrt{2})^2}$ $= \dfrac{3(\sqrt{5} + \sqrt{2})}{(5-2)}$ $= \d…

Question: Rationalize the denominators and simplify: $\dfrac{1}{√3 -2}$ Solution: Given, $= \dfrac{1}{√3 - 2}$ $= \dfrac{1}{√3 -2} × \dfrac{√3 +2}{√3 +2}$ $= \dfrac{1(√3+2)}{(√3}² - 2²}$ $= \dfrac{√3 + 2}{3 -4}$ $= \dfrac{√3 +2}{-1}$ $= - (√3 +2)$ $= -√3 - 2$ = Answer #SciPiPupil