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) - 6.261
(b) - 2.987
(c) - 8.571
(d) - 4.845
The correct answers to the above question in:
Answer: (d)
$√5/2 + 5/{3√5} - √45$
=$√5/2+{5×√5}/{3×5}-3√5$
=$√5/2+√5/3-3√5$
=${3√5+2√5-18√5}/6$
=${-13√5}/6={-13×2.236}/6$
=${-29.068}/6=-4.845$
Discuss Form
Read more simplifying roots with values Based Quantitative Aptitude Questions and Answers
Question : 1
If $√3$ = 1.732, then the value of ${9 +2√3}/√3$ is :
a) 7.296
b) 5.198
c) 7.169
d) 7.196
Answer »Answer: (d)
Expression =${9 +2√3}/√3$
=${(9+2√3)×√3}/{√3×√3}$
=${9√3+6}/3=3√3+2$
= 3 × 1.732 + 2 = 5.196 + 2
= 7.196
Question : 2
Evaluate : $16√{3/4} - 9√{4/3}$ if $√12$ = 3.46
a) 24.22
b) 13.84
c) 3.46
d) 10.38
Answer »Answer: (c)
Expression
$16√{3/4} - 9√{4/3}$ if $√12$ = 3.46
=$16√{{3×4}/{4×4}} - 9√{{4×3}/{3×3}}$
=${16√12}/4-{9√12}/3$
=$4√12-3√12$
=$√12$=3.46
Question : 3
Given $√2$ = 1.414. The value of $√8 +2√32 -3√128 +4√50$ is
a) 8.876
b) 8.426
c) 8.484
d) 8.526
Answer »Answer: (c)
$√8 +2√32 -3√128 +4√50$
=$2√2 +8√2 -3×8√2 +4×5√2$
=$2√2 +8√2 -24√2 +20√2$
= (2 + 8 -24 +20)$√2$
=6$√2$=6×1.414=8.484
Question : 4
If $√33$ = 5.745, then the value of $√{3/11}$ is approximately
a) 2.035
b) 6.32
c) 1
d) 0.5223
Answer »Answer: (d)
$√33$ = 5.745(Given)
$√{3/11}=√{{3×11}/{11×11}}=√33/11$
=${5.745}/11 ≈0.5223$
Question : 5
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 : 6
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
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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