Model 2 Simplification based on square & square root Practice Questions Answers Test with Solutions & More Shortcuts
simplification PRACTICE TEST [4 - EXERCISES]
Model 1 Simplification using VBODMAS
Model 2 Simplification based on square & square root
Model 3 Simplification based on cube & cube root
Model 4 Simplification with continued fraction
Question : 1 [SSC CPO Sub-Inspector 2010]
${√{24} + √{216}}/√{96}$ is equal to
a) 2$√6$
b) 4$√6$
c) $2/√6$
d) 2
Answer »Answer: (d)
${√{24} + √{216}}/√{96}$
= ${{2√{6} + 6√{6}}/{4√{6}} = {8√6}/{4√6}$ = 2
Question : 2 [SSC CGL Prelim 2000]
The value of ${√{80} - √{112}}/{√{45} - √{63}}$ is :
a) $1{3}/4$
b) 1$1/3$
c) $3/4$
d) 1$7/9$
Answer »Answer: (b)
${√{80} - √{112}}/{√{45} - √{63}}$
= ${√{16 × 5} - √{16 × 7}}/{√{9 × 5} - √{9 × 7}}$
= ${4√{5} - 4√{7}}/{3√{5} - 3√{7}} = {4(√{5} - √{7})}/{3(√{5} - √{7})$
= $4/3 = 1{1}/3$
Question : 3 [SSC CPO S.I.2003]
The value of ${(75.8)^2 - (55.8)^2}/20$ is
a) 40
b) 121.6
c) 20
d) 131.6
Answer »Answer: (d)
${(75.8)^2 - (55.8)^2}/20$
= ${(75.8 - 55.8)(75.8 + 55.8)}/20$
= ${20 × 131.6}/20$ = 131.6
Using Rule 8,
${(75.8)^2 - (55.8)^2}/{(75.8 - 55.8)}$
= 75.8 + 55.8 = 131.6
Question : 4
The simplified value of $√{900} + √{0.09} + √{0.000009}$ is
a) 30.297
b) 30.097
c) 30.27
d) 30.197
Answer »Answer: (a)
Expression
= $√{900} + √{0.09} - √{0.000009}$
= 30 + 0.3 - 0.003
= 30.297
Question : 5 [SSC CGL Prelim 2002]
The value of $√{{(6.1)^2 + (61.1)^2 + (611.1)^2}/{(0.61)^2 + (6.11)^2 + (61.11)^2}}$ is
a) 1.1
b) 10
c) 0.1
d) 100
Answer »Answer: (b)
$√{{(6.1)^2 + (61.1)^2 + (611.1)^2}/{(0.61)^2 + (6.11)^2 + (61.11)^2}}$
= $√{{(10 × 0.61)^2 + (10 × 6.11)^2 + (10 × 61.11)^2}/{(0.61)^2 + (6.11)^2 + (61.11)^2}}$
=$√{100}$ = 10
IMPORTANT quantitative aptitude EXERCISES
Model 2 Simplification based on square & square root Shortcuts »
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