Practice Simplifying roots with values - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Given that $√5$ = 2.24, then the value of ${3√5}/{2√5 -0.48}$ is
(a)
(b)
(c)
(d)
Expression=${3√5}/{2√5 -0.48}$
=${3×2.24}/{2×2.24-0.48}={6.72}/{4.48-0.48}$
=$6.72/4=1.68$
Q-2) If $√2$ = 1.4142… is given, then the value of $7/{(3 +√2)}$ correct upto two decimal places is
(a)
(b)
(c)
(d)
$7/{(3 +√2)}={7(3-√2)}/{(3+√2)(3-√2)}$
[Rationalising the denominator]
=${7(3-√2)}/{9-2}$
$[(a+b)(a-b)=a^2-b^2]$
=$3-√2$
= 3 - 1.4142 = 1.5858
= 1.59 (correct to two decimal places)
Q-3) If $√3$ = 1.732, then what is the value of ${4 +3√3}/{√{7 + 4 √3}}$ upto three places of decimal ?
(a)
(b)
(c)
(d)
${4 +3√3}/{√{7 + 4 √3}}$
${4 +3√3}/{√{7 + 4 √3}}={4+3√3}/{√{4+3+2×2×√3}}$
=${4+3√3}/{√(2+√3)^2}={4+3√3}/{2+√3}$
${(4+3√3)(2-√3)}/{(2+√3)(2-√3)}$
=$8-4√3+6√3-9$
=$2√3-1=2×1.732-1$
= 3.464 - 1 = 2.464
Q-4) Given that $√5$ = 2.236 and $√3$ = 1.732; the value of $1/{√5 +√3}$ is
(a)
(b)
(c)
(d)
Expression=$1/{√5 +√3}$
=$1/{√5 +√3}×{√5 -√3}/{√5 -√3}$
(Rationalising the denominator)
=${√5 -√3}/{5-3}={2.236-1.732}/2$
=$0.504/2=0.252$
Q-5) Given that $√2$ = 1.414; the value of $1/{√2 + 1}$ is
(a)
(b)
(c)
(d)
Expression
=$1/{√2 + 1}={√2 - 1}/{(√2 + 1)(√2 - 1)}$
=${√2-1}/{2-1}=√2-1$
= 1.414 - 1 = 0.414
Q-6) Given that $√3$ = 1.732, the value of ${3 +√6}/{5√3 - 2√12- √32+√ 50}$ is
(a)
(b)
(c)
(d)
Expression
=${3 +√6}/{5√3 - 2√12- √32+√ 50}$
=${3 +√6}/{5√3 - 2√{2×2×3}- √{2×2×2×2×2}+√{2×5×5}}$
=${3 +√6}/{5√3 - 4√{3}- 4√{2}+5√{2}}$
=${3 +√6}/{√3 +√2}={(3+√6)(√3-√2)}/{(√3+√2)(√3-√2)}$
[On rationalising the denominator]
=${3√3+√18-3√2-√12}/{3-2}$
=$3√3+3√2-3√2-2√3$
=$√3=1.732$
Q-7) If $√33$ = 5.745, then the value of $√{3/11}$ is approximately
(a)
(b)
(c)
(d)
$√33$ = 5.745(Given)
$√{3/11}=√{{3×11}/{11×11}}=√33/11$
=${5.745}/11 ≈0.5223$
Q-8) If $√3$ = 1.732, then the value of ${9 +2√3}/√3$ is :
(a)
(b)
(c)
(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
Q-9) Evaluate : $16√{3/4} - 9√{4/3}$ if $√12$ = 3.46
(a)
(b)
(c)
(d)
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
Q-10) Given $√2$ = 1.414. The value of $√8 +2√32 -3√128 +4√50$ is
(a)
(b)
(c)
(d)
$√8 +2√32 -3√128 +4√50$
=$2√2 +8√2 -3×8√2 +4×5√2$
=$2√2 +8√2 -24√2 +20√2$
= (2 + 8 -24 +20)$√2$
=6$√2$=6×1.414=8.484