Practice Largest and smallest value - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

$√{0.09}, √^3{0.064},$ 0.5 and $3/5$

$√{0.09}=0.3$

$√^3{0.064}=0.4$; 0.5;

$3/5$= 0.6

Clearly, $√{0.09}<√^3{0.064}<0.5<3/5$

0.16, $√{0.16}, (0.16)^2$, 0.04

$√{0.16}=0.4$

$(0.16)^2=0.0256$

Clearly,

0.0256 < 0.04 < 0.16 < $√{0.16}$

$3^50 , 4^40, 5^30$ and $6^20$

$3^50=(3^5)^10=(243)^10$

$4^40=(4^4)^10=(256)^10$

$5^30=(5^3)^10=(125)^10$

$6^20=(6^2)^10=(36)^10$

∴ Largest number =$4^40$

$2^60, 3^48, 4^36$ and $5^24$

$2^60 = (2^5)^12 =(32)^12$

$5^24 = (5^2)^12 =(25)^12$

$2^60 >5^24$

$3^48 =(3^4)^12 =(81)^12$

$3^48 >2^60$

$4^36 =(4^3)^12 = (64)^12$

$3^48$ is the largest number

$2^250=(2^5)^50=(32)^50$

$3^150=(3^3)^50=(27)^50$

$5^100=(5^2)^50=(25)^50$

$4^200=(4^4)^50=(256)^50$

∴ The smallest number =$(5)^100$

$√3, √^3{2}, √2$ and $√^3{4}$

LCM of 2 and 3 = 6

$√3 = (3)^{1/2}=3^{3/6}=(3^3)^{1/6}=√^6{27}$

$√^3{2} = √^6{2^2} =√^6{4}$

$√{2} = √^6{2^3} =√^6{8}$

$√^3{4} = √^6{4^2} =√^6{16}$

$√^6{12}, √^3{4}, √^4{5}, √3$

LCM of indices of surds

= LCM of 6, 3, 4 and 2 = 12

$√^6{12} =√^12{2^2}=√^12{144}$

$√^3{4} =√^12{4^4}=√^12{256}$

$√^4{5} =√^12{5^3}=√^12{125}$

$√3 =√^12{3^6}=√^12{729}$

The smallest surd = $√^4{5}$

$√^3{2}, √3, √^3{5}$ and 1.5

LCM of 3 and 2 = 6.

$√^3{2}=√^6{2^2}=√^6{4}$

$√3=√^6{27}$

$√^3{5}=√^6{25}$

1.5 =$√{2.25}=√^6{(2.225)^3}$

$2√3, 2√^4{5}, √8$ 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 =$√8$