model 4 simplifying roots with values Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (b)

${4 +3√3}/{√{7 + 4 √3}}$

${4 +3√3}/{√{7 + 4 √3}}={4+3√3}/{√{4+3+2×2×√3}}$

=${4+3√3}/{√(2+√3)^2}={4+3√3}/{2+√3}$

${(4+3√3)(2-√3)}/{(2+√3)(2-√3)}$

=$8-4√3+6√3-9$

=$2√3-1=2×1.732-1$

= 3.464 - 1 = 2.464

Answer: (d)

Expression=$1/{√5 +√3}$

=$1/{√5 +√3}×{√5 -√3}/{√5 -√3}$

(Rationalising the denominator)

=${√5 -√3}/{5-3}={2.236-1.732}/2$

=$0.504/2=0.252$

Answer: (c)

Expression

=$1/{√2 + 1}={√2 - 1}/{(√2 + 1)(√2 - 1)}$

=${√2-1}/{2-1}=√2-1$

= 1.414 - 1 = 0.414

Answer: (d)

Expression

=$2√2 + √2 + 1/{2 + √2}+ 1/{ √2 - 2}$

=$2√2 + √2 + (1/{2 + √2}- 1/{ √2 - 2})$

=$2√2 + √2 + ({2 -√2-2-√2}/{(2+√2)(2-√2)})$

=$2√2+√2+{-2√2}/{4-2}$

=$2√2+√2-√2=2√2$

= 2 × 1.4142 = 2.8284

Answer: (a)

Expression

=${3 +√6}/{5√3 - 2√12- √32+√ 50}$

=${3 +√6}/{5√3 - 2√{2×2×3}- √{2×2×2×2×2}+√{2×5×5}}$

=${3 +√6}/{5√3 - 4√{3}- 4√{2}+5√{2}}$

=${3 +√6}/{√3 +√2}={(3+√6)(√3-√2)}/{(√3+√2)(√3-√2)}$

[On rationalising the denominator]

=${3√3+√18-3√2-√12}/{3-2}$

=$3√3+3√2-3√2-2√3$

=$√3=1.732$