model 1 find largest and smallest value Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (a)

$√2, √^6{3}, √^3{4}, √^4{5}$

LCM of 2, 6, 3, 4 = 12

$√2=√^12{2^6}=√^12{64}$

$√^6{3}=√^12{3^2}=√^12{9}$

$√^3{4}=√^12{4^4}=√^12{256}$

$√^4{5}=√^12{5^3}=√^12{125}$

Clearly,

$√^12{9}<√^12{64}<√^12{125}<√^12{256}$

∴ $√^6{3}<√2<√^4{5}<√^3{4}$

Answer: (a)

$2√3, 2√^4{5}, √8$ and $3√2$

The orders of the surds are 2, 4, 2 and 2. Their LCM = 4

We convert each surd into a surd of order 4.

$2√3=√{4×3}=√12=√^4(12)^2=√^4{144}$

$2√^4{5}=√^4{2^4×5}=√^4{80}$

$3√2=√18=√^4(18)^2=√^4{324}$

$√8=√^4{64}$

Hence, the least number =$√8$

Answer: (a)

$(2.89)^{0.5}, 2 - (0.5)^2, 1 + {0.5}/{1 - 1/2}, √3$

$(2.89)^{0.5}=(2.89)^{5/10}$

=$√{2.89}=1.7$

=$2 - (0.5)^2=2-0.25=1.75$

$1+{0.5}/{1-1/2}=1+{0.5}/{1/2}$

=$1+{0.5}/{0.5}=1+1=2$

$√3$ =1.732

Answer: (c)

$√^4{3}, √^5{4}, √^10{12}$, 1

LCM of indices of surds = 20

$√^4{3}=√^20{3^5}=√^20{243}$

$√^5{4}=√^20{4^4}=√^20{256}$

$√^10{12}=√^20{144}$

Answer: (d)

$√8 +√5, √7+√6, √{10}+√3$ and $√{11}+√2$

Here,

$(√8 +√5)^2 =(√8)^2+(√5)^2+2×√8×√5$

=$8+5+2×√{8×5}$

=$13+2√40$

Similarly,

$(√7+√6)^2=7+6+2×√{7×6}$

=$13+2√42$

$(√{10}+√3)^2=10+3+2×√{10×3}$

=$13+2√30$,

$(√{11}+√2)^2=11+2+2√{11×2}$

=$13+2√22$

Clearly, 13 + 2$√22$ is the smallest among these.

∴ $√11 + √2$ is the smallest.