model 2 based on simplification Section-Wise Topic Notes With Detailed Explanation And Example Questions

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: (b)

Expression

= $(256)^{0.16} × (16)^{0.18}$

= $(4)^{4×0.16} × (4)^{2×0.18}$

= $(4)^{0.64} × (4)^{0.36}$

= $(4)^{0.64+0.36} = (4)^1$ = 4

Answer: (d)

? = $(√8 - √4 - √2)$

= $(2√2 - 2 - √2) = √2 - 2$

Answer: (a)

$2√^3{32} - 3√^3{4} + √^3{500}$

Expression

= $2√^3{8 × 4} - 3√^3{4} + √^3{125 × 4}$

= $2×2√^3{4} - 3√^3{4} + 5√^3{4} = 6√^3{4}$