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) 4
(b) 5$1/2$
(c) 3$1/3$
(d) 21$1/3$
The correct answers to the above question in:
Answer: (a)
$8^{2/3} = (2^3)^{2/3}$
= $2^{3×2/3} = 2^2 = 4$
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Read more simplification problems Based Quantitative Aptitude Questions and Answers
Question : 1
$(0.04)^{ - (1.5)}$ is equal to
a) 60
b) 25
c) 5
d) 125
Answer »Answer: (d)
Expression = $(0.04)^{ - 1.5}$
= $1/(0.04)^{1.5} = 1/(0.04)^{3/2}$
= $1/(0.04 × 0.04 × 0.04)^{1/2}$
= $1/√{0.0000064}$
= $1/{0.008} = 1000/8 = 125$
Question : 2
The value of $(3 + 2√2)^{- 3} + (3 -2√2)^{ - 3}$ is
a) 108
b) 189
c) 198
d) 180
Answer »Answer: (c)
We know that
$a^3 + b^3 = (a + b)^3 - 3ab (a + b)$
Now
$(3 + 2√2)^{- 3} + (3 -2√2)^{ - 3}$
= $1/(3 + 2√2)^{3} + 1/(3 - 2√2)^{3}$
= ${(3 - 2√2)^{3} + (3 + 2√2)^{3}}/{(3 + 2√2)^{3} ×(3 - 2√2)^{3}}$
= ${(3 - 2√2 + 3 + 2√2)^3 - 3(3 - 2√2)(3 + 2√2)(3 - 2√2 + 3 + 2√2)}/[(3 + 2√2)(3-2√2)]^3$
= ${(6)^3 - 3(9-8)(6)}/1$
= 216 - 18 = 198
Question : 3
$(1/2)^{- 1/2}$ is equal to
a) - $√2$
b) $1/√2$
c) $√2$
d) 2$ √2$
Answer »Answer: (c)
$(1/2)^{- 1/2} = (2)^{1/2} = √2$
Question : 4
The value of $√{2}^4 + √^3{64} + √^4{2^8}$ is :
a) 18
b) 12
c) 24
d) 16
Answer »Answer: (b)
? = $√{2}^4 + √^3{64} + √^4{2^8}$
= $2^{4×1/2} + 4^{3×1/3} + 2^{8×1/4}$
= $2^2 + 4 + 2^2$
= 4 + 4 + 4 = 12
Question : 5
$(3 + 1/√3 + 1/{3 + √3} + 1/{√3 - 3})$ is equal to
a) $3 + √3$
b) 1
c) $3 - √3$
d) 3
Answer »Answer: (d)
Expression
= $3+1/√3+1/{3+√3}+1/{√3-3}$
= $3+1/√3+1/{3+√3}-1/{√3-3}$
= $3+1/√3+({3-√3-3-√3}/{(3+√3)(3-√3)})$
= $3+1/√3+{-2√3}/{9-3} = 3+1/√3 -√3/3$
= $3+1/√3-1/√3 = 3$
Question : 6
The simplified form of $2/{√7 + √5} + 7/{√{12} - √5} - 5/{√{12} - √7}$ is :
a) 1
b) 5
c) 0
d) 2
Answer »Answer: (c)
$2/{√7 + √5} + 7/{√{12} - √5} - 5/{√{12} - √7}$
First term = $2/{√7 + √5}$
= ${2 ×(√7 - √5)}/{(√7 + √5)(√7 - √5)}$
= ${2(√7 - √5)}/{7-5} = √7 -√5$
Second term = $7/{√{12} - √5}$
= ${7(√{12}+√5)}/{(√{12}-√{5})(√{12}+√5)}$
=${7(√{12}+√5)}/{12-5}$
= ${7(√{12} +√{5})}/{7} = √{12}+√5$
Third term = $5/{√{12}-√7}$
= ${5(√{12}+√7)}/{(√{12}-√7)(√{12}+√7)}$
= ${5(√{12}+√7)}/{12- 7} = √{12} +√7$
Expression
= $(√7 - √5) + (√{12} +√5) - (√{12}+√7)$
= $√7 -√5 +√{12} +√5 - √{12} -√7 = 0$
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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