Model 2 Simplification Based On Square & Square Root Practice Questions Answers Test With Solutions & More Shortcuts

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: (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: (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: (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: (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: (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

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