model 2 based on simplification Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on power, indices and surds topic of quantitative aptitude
(a) 3
(b) 1
(c) 8
(d) 2
The correct answers to the above question in:
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
Discuss Form
Read more simplification problems Based Quantitative Aptitude Questions and Answers
Question : 1
$√{8 - 2 √{15}}$ is equal to :
a) $√5 - √3$
b) $√5 + √3$
c) $3 - √5$
d) $5 - √3$
Answer »Answer: (a)
Expression=$√{8 - 2 √{15}}$
= $√{5+3-2√{5}×√{3}}$
= $√{(√5)^2+(√3)^2-2√5×√3}$
= $√{(√5-√3)^2} = √5-√3$
Question : 2
$√5/{√3 + √2} - {3√3}/{√5 + √2} + {2√2}/{√5 + √3}$ is equal to :
a) $2√10$
b) 0
c) $2√6$
d) $2√15$
Answer »Answer: (b)
$√5/{√3 + √2} - {3√3}/{√5 + √2} + {2√2}/{√5 + √3}$
$√5/{√3 + √2} = {√5(√3 - √2)}/{(√3 + √2)(√3 - √2)}$
= ${√{15} - √{10}}/{3 - 2} = √{15} - √{10}$
${3√3}/{√5 + √2} = {3√3}/{√5 + √2} × {√5 - √2}/{√5 - √2}$
= ${3√3(√5 - √2)}/{5-2} = √{15} - √6$
${2√2}/{√5 + √3} = {2√2(√5 - √3)}/{(√5 + √3)(√5 - √3)}$
= ${2√2(√5 -√3)}/{5 - 3} = √{10} - √6$
Expression
= $(√{15} - √{10}) - (√{15} - √6) + (√{10} - √6)$
= $√{15} - √{10} - √{15} + √6 + √{10} - √6 = 0$
Question : 3
a) 1.50
b) 1.00
c) 2.25
d) 1.25
Answer »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
Question : 4
$√{ √^3{0.004096}}$ 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 $√{5 + 2√{6}} - 1/{√{5 + 2√6}}$ 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 : 6
$(16^{0.16} × 2^{0.36})$ is equal to
a) 32
b) 2
c) 64
d) 16
Answer »Answer: (b)
$(16^{0.16} × 2^{0.36})$
= $(16^{16/100} × 2^{36/100})$
= $(2^{4×16/100} × 2^{36/100})$
= $(2^{64/100 + 36/100}) = (2^{100/100}) = 2$
GET power, indices and surds PRACTICE TEST 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
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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