model 4 simplifying roots with values Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11

Given that $√5$ = 2.24, then the value of ${3√5}/{2√5 -0.48}$ is

a) 168

b) 16.8

c) 0.168

d) 1.68

Answer: (d)

Expression=${3√5}/{2√5 -0.48}$

=${3×2.24}/{2×2.24-0.48}={6.72}/{4.48-0.48}$

=$6.72/4=1.68$

Question : 12

If $√15$ = 3.88, then what is the value of $√{5/3}$

a) 1.295

b) 1.29

c) 1.29$\ov{3}$

d) 1.2934

Answer: (c)

$√15$=3.88(Given)

Now, $√{5/3}=√{{5×3}/{3×3}}=√15/3$

=$3.88/3=1.29\ov{3}$

Question : 13 [SSC DEO 2008]

If $√3$ =1.732, is given, then the value of ${2+ √3}/{2 -√3}$ is

a) 13.925

b) 12.928

c) 11.732

d) 13.928

Answer: (d)

Expression

=${2+ √3}/{2 -√3}={(2+ √3)(2+ √3)}/{(2- √3)(2+ √3)}$

[On rationalising the denominator]

=${(2+√3)^2}/{4-3}=(2+√3)^2$

=$2^2+(√3)^2+2×2×√3$

=$4+3+4√3$

= 7 + 4 × 1.732 = 7 + 6.928

= 13.928

Question : 14 [SSC CHSL 2015]

If $√7$ = 2.646, then the value of $1/√28$ up to three places of decimal is :

a) 0.189

b) 0.187

c) 0.183

d) 0.185

Answer: (a)

$1/√28=1/{2√7}$

=$√7/{2√7×√7}=√7/14$

=$2.646/14=0.189$

Question : 15 [SSC CGL Tier-II 2015]

If $√5329$ = 73, then the value of $√5329 + √53.29 + √0.5329 + √0.005329 + √0.00005329$ is

a) 81.1013

b) 81.1103

c) 81.1003

d) 81.0113

Answer: (b)

$√5329 + √53.29 + √0.5329 + √0.005329 + √0.00005329$

$√5329$ = 73

= 73 + 7.3 + 0.73 + 0.073 + 0.0073

= 81.1103

IMPORTANT quantitative aptitude EXERCISES

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