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

Question : 6

If $√33$ = 5.745, then the value of $√{3/11}$ is approximately

a) 2.035

b) 6.32

c) 1

d) 0.5223

Answer: (d)

$√33$ = 5.745(Given)

$√{3/11}=√{{3×11}/{11×11}}=√33/11$

=${5.745}/11 ≈0.5223$

Question : 7 [SSC CAPFs 2016]

If $√5$ = 2.236, then what is the value of $√5/2 + 5/{3√5} - √45$ ?

a) - 6.261

b) - 2.987

c) - 8.571

d) - 4.845

Answer: (d)

$√5/2 + 5/{3√5} - √45$

=$√5/2+{5×√5}/{3×5}-3√5$

=$√5/2+√5/3-3√5$

=${3√5+2√5-18√5}/6$

=${-13√5}/6={-13×2.236}/6$

=${-29.068}/6=-4.845$

Question : 8 [SSC CGL Tier-I 2016]

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: (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 : 9 [SSC CPO S.I.2009]

Evaluate : $16√{3/4} - 9√{4/3}$ if $√12$ = 3.46

a) 24.22

b) 13.84

c) 3.46

d) 10.38

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 : 10 [SSC CGL Prelim 2003]

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: (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

IMPORTANT quantitative aptitude EXERCISES

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