model 1 find largest and smallest value Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

$(0.5)^2, √{0.49}, √^3{0.008}, 0.23$

$(0.5)^2$=0.25

$√{0.49}$=0.7

$√^3{0.008}$=0.2

0.23 = 0.23

∴ $√{0.49}>(0.5)^2>0.23>√^3{0.008}$

Answer: (d)

$√{0.09}, √^3{0.064},$ 0.5 and $3/5$

$√{0.09}=0.3$

$√^3{0.064}=0.4$; 0.5;

$3/5$= 0.6

Clearly, $√{0.09}<√^3{0.064}<0.5<3/5$

Answer: (c)

$2^60, 3^48, 4^36$ 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

Answer: (d)

$√^2{8}, √^4{13}, √^5{16}, √^10{41}$

LCM of 2, 4, 5 and 10 = 20

$√^2{8}=√^20{8^10}; √^4{13}=√^20{13^5}$

$√^5{16}=√^20{16^4}; √^10{41}=√^20{41^2}$

Clearly, $√^2{8}$ is the largest.

Answer: (c)

$3^50 , 4^40, 5^30$ 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 =$4^40$