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

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)

$2√^3{32} - 3√^3{4} + √^3{500}$

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)

? = $(√8 - √4 - √2)$

= $(2√2 - 2 - √2) = √2 - 2$

Answer: (d)

$(16)^{0.16} × (16)^{0.04} × (2)^{0.2}$

= $(2^4)^{0.16} × (2^4)^{0.04} × (2)^{0.2}$

= $2^{0.64} × 2^{0.16} × 2^{0.2}$

= $(2)^{0.64+0.16+0.2}$ = 2

Answer: (d)

Expression

= $12/{3 + √5 + 2√2}$

= ${12(3+√5-2√2)}/{[(3+√5)+2√2][(3+√5)-2√2]}$

[Rationalising the denominator]

= ${12(3+√5-2√2)}/{(3+√5)^2- (2√2)^2}$

= ${12(3+√5-2√2)}/{9+5+6√5-8}$

= ${12(3√5-2√2)}/{6√5+6}$

= ${2(3+√5-2√2)}/{√5+1}$

= ${2(3+√5-2√2)(√5-1)}/{(√5+1)(√5-1)}$

= ${2(3√5+5-2√{10}-3-√5+2√2)}/{5-1}$

= ${2(2√5+2√2-2√{10}+2)}/4$

= ${2×2(√5+√2-√{10}+1)}/4$

= $1+√5+√2-√{10}$

Answer: (b)

$1/{√{3.25} + √{2.25}} + 1/{√{4.25} + √{3.25}} + 1/{√{5.25} + √{4.25}} + 1/{√{6.25} + √{5.25}}$

$1/{√{3.25} + √{2.25}}$

= $1/(√{3.25} + √{2.25})×{{√{3.25} - √{2.25}}/{√{3.25} - √{2.25}}}$

= ${√{3.25} - √{2.25}}/{3.25 - 2.25} = √{3.25} - √{2.25}$

Similarly

$1/{√{4.25} + √{3.25}}= √{4.25} - √{3.25}$

$1/{√{5.25} + √{4.25}}= √{5.25} - √{4.25}$

$1/{√{6.25} + √{5.25}}= √{6.25} - √{5.25}$

Expression

=$√{3.25} - √{2.25} +√{4.25} - √{3.25} +√{5.25} - √{4.25} +√{6.25} - √{5.25}$

= $√{6.25} - √{2.25}$

= 2.5 - 1.5 =1