model 2 based on simplification Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Expression = $(0.04)^{ - 1.5}$

= $1/(0.04)^{1.5} = 1/(0.04)^{3/2}$

= $1/(0.04 × 0.04 × 0.04)^{1/2}$

= $1/√{0.0000064}$

= $1/{0.008} = 1000/8 = 125$

Answer: (c)

We know that

$a^3 + b^3 = (a + b)^3 - 3ab (a + b)$

Now

$(3 + 2√2)^{- 3} + (3 -2√2)^{ - 3}$

= $1/(3 + 2√2)^{3} + 1/(3 - 2√2)^{3}$

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

= ${(3 - 2√2 + 3 + 2√2)^3 - 3(3 - 2√2)(3 + 2√2)(3 - 2√2 + 3 + 2√2)}/[(3 + 2√2)(3-2√2)]^3$

= ${(6)^3 - 3(9-8)(6)}/1$

= 216 - 18 = 198

Answer: (c)

$(1/2)^{- 1/2} = (2)^{1/2} = √2$

Answer: (a)

$1/{√3 + √4} + 1/{√4 + √5} +1/{√5 + √6} +1/{√6 + √7} +1/{√7 + √8} +1/{√8 + √9}$

$1/{√3 + √4}$

= $1/{√3 + √4}×{√4 - √3}/{√4-√3}$

= ${√4-√3}/{4-3} =√4-√3$

Similarly,

$1/{√4+√5}=√5-√4$

$1/{√5+√6}=√6-√5$

$1/{√6+√7}=√7-√6$

$1/{√7+√8}=√8-√7$

$1/{√8+√9}=√9-√8$

Expression

= $√4 -√3+√5-√4+√6-√5+√7-√6+√8-√7+√9-√8$

= $√9-√3 = 3-√3$

Answer: (d)

$16^{3/4} = (4^2)^{3/4}$

= $4^{2×3/4} = 4^{3/2} = 2^{2×3/2} = 2^3 = 8$