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

Answer: (d)

$(16^{3/2} + 16^{-3/2})$

= $(4^2)^{3/2} + 1/(16)^{3/2}$

= $4^{2×3/2} + 1/4^{2×3/2} = 4^3 + 1/4^3$

= $64 + 1/64 = {4096 + 1}/64 = 4097/64$

Answer: (c)

$2/{√7 + √5} + 7/{√{12} - √5} - 5/{√{12} - √7}$

First term = $2/{√7 + √5}$

= ${2 ×(√7 - √5)}/{(√7 + √5)(√7 - √5)}$

= ${2(√7 - √5)}/{7-5} = √7 -√5$

Second term = $7/{√{12} - √5}$

= ${7(√{12}+√5)}/{(√{12}-√{5})(√{12}+√5)}$

=${7(√{12}+√5)}/{12-5}$

= ${7(√{12} +√{5})}/{7} = √{12}+√5$

Third term = $5/{√{12}-√7}$

= ${5(√{12}+√7)}/{(√{12}-√7)(√{12}+√7)}$

= ${5(√{12}+√7)}/{12- 7} = √{12} +√7$

Expression

= $(√7 - √5) + (√{12} +√5) - (√{12}+√7)$

= $√7 -√5 +√{12} +√5 - √{12} -√7 = 0$

Answer: (d)

Expression

= $3+1/√3+1/{3+√3}+1/{√3-3}$

= $3+1/√3+1/{3+√3}-1/{√3-3}$

= $3+1/√3+({3-√3-3-√3}/{(3+√3)(3-√3)})$

= $3+1/√3+{-2√3}/{9-3} = 3+1/√3 -√3/3$

= $3+1/√3-1/√3 = 3$

Answer: (b)

? = $√{2}^4 + √^3{64} + √^4{2^8}$

= $2^{4×1/2} + 4^{3×1/3} + 2^{8×1/4}$

= $2^2 + 4 + 2^2$

= 4 + 4 + 4 = 12

Answer: (a)

$8^{2/3} = (2^3)^{2/3}$

= $2^{3×2/3} = 2^2 = 4$