Practice Problems based on squares and roots - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) On simplification of ${(2.644)^2 - (2.356)^2}/{0.288}$ we get :
(a)
(b)
(c)
(d)
? = ${(2.644)^2 - (2.356)^2}/{0.288}$
= ${(2.644 - 2.356)(2.644 + 2.356)}/{0.288}$
= ${0.288 × 5}/{0.288} = 5$
Using Rule 8,${a^2 - b^2}/{a - b} = a+b or, {a^2 - b^2}/{a + b} = a-b$
${(2.644)^2 - (2.356)^2}/{0.288}$
= ${(2.644)^2 - (2.356)^2}/{2.644 + 2.356}$
= (2.644 + 2.356) = 5
Q-2) The value of $√{5+ √{11 + √{19 + √{29 + √{49}}}}}$ is
(a)
(b)
(c)
(d)
$√{5+ √{11 + √{19 + √{29 + √{49}}}}}$
$√{5+ √{11 + √{19 + √{29 + 7}}}}$
$√{5+ √{11 + √{19 + 6}}}$
$√{5+ √{11 + √{25}}}$
$√{5+ √{11 + 5}}$
$√{5+ 4} = √9$ = 3
Q-3) The value of $(3 + √{8}) + 1/{3 - √{8}} - (6 + 4√{2})$ is
(a)
(b)
(c)
(d)
${1/{3 - √8}} = {3 + √8}/{(3 - √8)(3 + √8)}$
(Rationalising the denominator)
= ${3 + √8}/{9 - 8} = 3 + √8$
Expression
= $3 + √{8} + 3 + √{8} - 6 - 4√{2}$
= $6 + 2√{8} - 6 - 4√{2} = 2√{8} - 4√{2}$
= $2 × 2√{2} - 4√{2} = 0$
Q-4) The square root of : ${(0.75)^3}/{1 - 0.75} + [0.75 + (0.75)^2 + 1]$ is :
(a)
(b)
(c)
(d)
Expression
= ${(0.75)^3 + (1 - 0.75)((0.75)^2 + 0.75 × 1 + {1}^2)}/{1 - 0.075}$
= ${(0.75)^3 + 1^3 - (0.75)^3}/{0.25}$
= $1/{0.25} = 100/25 = 4$
Required square root = $√{4} = 2$
Q-5) Simplify $√{[(12.1)^2 - (8.1)^2] + [(0.25)^2 + (0.25)(19.95)]}$
(a)
(b)
(c)
(d)
$√{{20.2 × 4}/{0.25 × 20.2}} = √{4/{0.25}}$
= $√{400/25} = √{16}$ = 4
Q-6) Simplification of ${(3.4567)^2 - (3.4533)^2}/{0.0034}$ yields the result :
(a)
(b)
(c)
(d)
? = ${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$
= ${6.9100 × 0.0034}/{0.0034}$ = 6.91
Using Rule 8,
${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$
= ${{3.4567}^2 - {3.4533}^2}/{(3.4567 - 3.4533)}$
= 3.4567 + 3.4533 = 6.91
Q-7) $[2√{54} - 6√{2/3} - √{96}]$ is equal to
(a)
(b)
(c)
(d)
Expression
= $2√{54} - 6√{2/3} - √{96}$
= $2√{9 × 6} - √{{2 × 6 × 6}/3} - √{16 × 6}$
= $2 × 3√{6} - 2√{6} - 4√{6}$ = 0
Q-8) The value of ${(75.8)^2 - (55.8)^2}/20$ is
(a)
(b)
(c)
(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
Q-9) The value of $√{{(0.1)^2 + (0.01)^2 + (0.009)^2}/{(0.01)^2 + (0.001)^2 + (0.0009)^2}}$ is :
(a)
(b)
(c)
(d)
$√{{(0.1)^2 + (0.01)^2 + (0.009)^2}/{(0.01)^2 + (0.001)^2 + (0.0009)^2}}$
= $√{{0.01 + 0.0001 + 0.000081}/{0.0001 + 0.000001 + 0.00000081}}$
= $√{{0.010181}/{0.00010181}} = √{100}$ = 10
Q-10) $√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$ is equal to
(a)
(b)
(c)
(d)
Expression
= $√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$
= $√{{9 × 36 × 16 × 8}/{2 × 8 × 2}}$
= 3 × 2 × 3 × 2 = 36