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

Question : 11 [SSC SO 2005]

When $(4 + √7)$ is presented in the form of perfect square it will be equal to

a) $(1/√2(√7 + 1))^2$

b) $(2 + √7)^2$

c) $(√3 + √4)^2$

d) $(√7/2 + 1/2)^2$

Answer: (a)

$(4 + √7) = {8+2√7}/2$

= ${7+1+2×√7×1}/2$

= ${(√7)^2 + (1)^2 + 2 ×√7 × 1}/2$

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

Question : 12 [SSC SO 2003]

The approximate value of ${3√{12}}/{2√{28}}$ ÷ ${2√{21}}/√{98}$ is

a) 1.6026

b) 1.0727

c) 1.6007

d) 1.0606

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

Question : 13

$2√^3{32} - 3√^3{4} + √^3{500}$ is equal to :

a) $6√^3{4}$

b) $4√^3{6}$

c) 916

d) $3√{24}$

Answer: (a)

$2√^3{32} - 3√^3{4} + √^3{500}$

Expression

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

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

Question : 14

$(√8 - √4 - √2)$ equals :

a) 2

b) 2 - $√2$

c) - 2

d) $√2$ - 2

Answer: (d)

? = $(√8 - √4 - √2)$

= $(2√2 - 2 - √2) = √2 - 2$

Question : 15 [SSC CGL Prelim 2002]

The value of $(256)^{0.16} × (16)^{0.18}$ is :

a) 16

b) 4

c) 256

d) - 4

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

IMPORTANT quantitative aptitude EXERCISES

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