model 2 based on simplification Practice Questions Answers Test with Solutions & More Shortcuts
power, indices and surds PRACTICE TEST [5 - EXERCISES]
model 1 find largest and smallest value
model 2 based on simplification
model 3 based on positive and negative exponent
model 4 simplifying roots with values
model 5 simplifying roots of roots
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 »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 »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 »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 »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 »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
model 2 based on simplification Shortcuts »
Click to Read...model 2 based on simplification Online Quiz
Click to Start..power, indices and surds Shortcuts and Techniques with Examples
-
model 1 find largest and smallest value
Defination & Shortcuts … -
model 2 based on simplification
Defination & Shortcuts … -
model 3 based on positive and negative exponent
Defination & Shortcuts … -
model 4 simplifying roots with values
Defination & Shortcuts … -
model 5 simplifying roots of roots
Defination & Shortcuts …
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