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

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)

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

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

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

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

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: (a)

$2√^3{32} - 3√^3{4} + √^3{500}$

Expression

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

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

Answer: (d)

${3√{12}}/{2√{28}}$ ÷ ${2√{21}}/√{98}$

Expression

= ${3×√{12}}/{2×√{28}}$ × $√{98}/{2×√{21}}$

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

= ${3√2}/4 = {3 × 1.414}/4$

= 1.0605 ≈1.0606

Answer: (a)

$(4 + √7) = {8+2√7}/2$

= ${7+1+2×√7×1}/2$

= ${(√7)^2 + (1)^2 + 2 ×√7 × 1}/2$

= ${(√7+1)^2}/(√2)^2 = (1/{√2}(√7+1))^2$