model 4 simplifying roots with values 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) 0.372
(b) 0.362
(c) 0.504
(d) 0.252
The correct answers to the above question in:
Answer: (d)
Expression=$1/{√5 +√3}$
=$1/{√5 +√3}×{√5 -√3}/{√5 -√3}$
(Rationalising the denominator)
=${√5 -√3}/{5-3}={2.236-1.732}/2$
=$0.504/2=0.252$
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Read more simplifying roots with values Based Quantitative Aptitude Questions and Answers
Question : 1
Given that $√2$ = 1.414; the value of $1/{√2 + 1}$ is
a) 5.414
b) 3.414
c) 0.414
d) 2.414
Answer »Answer: (c)
Expression
=$1/{√2 + 1}={√2 - 1}/{(√2 + 1)(√2 - 1)}$
=${√2-1}/{2-1}=√2-1$
= 1.414 - 1 = 0.414
Question : 2
If $ √2$ = 1.4142, find the value of $2√2 + √2 + 1/{2 + √2}+ 1/{ √2 - 2}$
a) 2.4142
b) 28.284
c) 1.4144
d) 2.8284
Answer »Answer: (d)
Expression
=$2√2 + √2 + 1/{2 + √2}+ 1/{ √2 - 2}$
=$2√2 + √2 + (1/{2 + √2}- 1/{ √2 - 2})$
=$2√2 + √2 + ({2 -√2-2-√2}/{(2+√2)(2-√2)})$
=$2√2+√2+{-2√2}/{4-2}$
=$2√2+√2-√2=2√2$
= 2 × 1.4142 = 2.8284
Question : 3
Given that $√3$ = 1.732, the value of ${3 +√6}/{5√3 - 2√12- √32+√ 50}$ is
a) 1.732
b) 1.414
c) 4.899
d) 2.551
Answer »Answer: (a)
Expression
=${3 +√6}/{5√3 - 2√12- √32+√ 50}$
=${3 +√6}/{5√3 - 2√{2×2×3}- √{2×2×2×2×2}+√{2×5×5}}$
=${3 +√6}/{5√3 - 4√{3}- 4√{2}+5√{2}}$
=${3 +√6}/{√3 +√2}={(3+√6)(√3-√2)}/{(√3+√2)(√3-√2)}$
[On rationalising the denominator]
=${3√3+√18-3√2-√12}/{3-2}$
=$3√3+3√2-3√2-2√3$
=$√3=1.732$
Question : 4
If $√3$ = 1.732, then what is the value of ${4 +3√3}/{√{7 + 4 √3}}$ upto three places of decimal ?
a) 3.023
b) 2.464
c) 0.023
d) 0.464
Answer »Answer: (b)
${4 +3√3}/{√{7 + 4 √3}}$
${4 +3√3}/{√{7 + 4 √3}}={4+3√3}/{√{4+3+2×2×√3}}$
=${4+3√3}/{√(2+√3)^2}={4+3√3}/{2+√3}$
${(4+3√3)(2-√3)}/{(2+√3)(2-√3)}$
=$8-4√3+6√3-9$
=$2√3-1=2×1.732-1$
= 3.464 - 1 = 2.464
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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