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 : 1 [SSC CPO S.I.2003]
The value of ${(243)^{0.13} × (243)^{0.07}}/{(7)^{0.25} × (49)^{0.075} × (343)^{0.2}}$
a) 1$3/7$
b) $3/7$
c) 2$2/7$
d) $7/3$
Answer »Answer: (b)
${(243)^{0.13} × (243)^{0.07}}/{(7)^{0.25} × (49)^{0.075} × (343)^{0.2}}$
Expression
= ${(243)^{0.13+0.07}/{(7)^{0.25} × (7×7)^{0.075} × (7×7×7)^{0.2}}$
= ${(3^5)^{0.2}/{(7)^{0.25} × (7)^{2×0.075} × (7)^{3×0.2}}$
= ${(3)^{5×0.2}/{(7)^{0.25 + 0.15 + 0.6} = 3/7$
Question : 2
$(16^{0.16} × 2^{0.36})$ is equal to
a) 32
b) 2
c) 64
d) 16
Answer »Answer: (b)
$(16^{0.16} × 2^{0.36})$
= $(16^{16/100} × 2^{36/100})$
= $(2^{4×16/100} × 2^{36/100})$
= $(2^{64/100 + 36/100}) = (2^{100/100}) = 2$
Question : 3
The value of $√{5 + 2√{6}} - 1/{√{5 + 2√6}}$ is :
a) 1+ $√5$
b) 2$√2$
c) $√5 - 1$
d) 2$√3$
Answer »Answer: (b)
$√{5 + 2√{6}}$
= $√{3 + 2 + 2 × √{3} × √{2}}$
= $√{(√{3} + √{2})^2} = √3 + √2$
$1/√{5 + 2√{6}} = √3 - √2$
Hence, Expression
= $√3 + √2 - √3 + √2 = 2√2$
Question : 4 [SSC CGL Prelim 2003]
$√{ √^3{0.004096}}$ is equal to
a) 0.04
b) 4
c) 0.004
d) 0.4
Answer »Answer: (d)
$√{ √^3{0.004096}}$
= $(√^3{0.004096})^{1/2}$
= $({0.004096})^{1/3×1/2}$
= $(4096/1000000)^{1/6} = ((4/10)^6)^{1/6}$
= $(4/10)^{6×1/6} = 4/10 =0.4$
Question : 5
The value of : $√{ - √{3} + √{3 + 8√{7 + 4√{3}}}}$ is
a) 3
b) 1
c) 8
d) 2
Answer »Answer: (d)
$√{ - √{3} + √{3 + 8√{7 + 4√{3}}}}$
= $√{ - √{3} + √{3 + 8√{4 + 3 + 2 × 2 × √{3}}}}$
= $√{ - √{3} + √{3 + 8√{(2)^2 + (√3)^2 + 2 × 2 × √{3}}}}$
= $√{ - √{3} + √{3 + 8√{(2 × √{3})^2}}}$
= $√{ - √{3} + √{3 + 8(2 × √{3})}}$
= $√{ - √{3} + √{3 + 16 +8√{3}}}$
= $√{-√{3} + √{(√3)^2 + (4)^2 + 2 × 4 √{3}}}$
=$√{-√{3} + √{(4 + √3)^2}}$
= $√{-√{3} + 4 +√{3}} = √4$ = 2
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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