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

Answer: (c)

$√2, √^3{3}, √^6{6}, √^5{5}$

LCM of 2, 3, 6 & 5 = 30

$2^{1/2} = 2^{15/30} = √^30{2^15}=32768$

$3^{1/3} = 3^{10/30} = √^30{3^10}= 59049$

$6^{1/6} = 6^{5/30} = √^30{6^5}=7776$

$5^{1/5} = 5^{6/30} = √^30{5^5}$= 15625

Therefore, $√^3{3}$ is the greatest.

Answer: (a)

$√^3{2}, √3, √^3{5}$ 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 =$√{2.25}=√^6{(2.225)^3}$

Answer: (d)

$(√{19} - √{17}),(√{13} -√{11}),(√7 -√5)$ and $(√5-√3)$

$√{19} - √{17}$

=${(√19-√17)×(√19+√17)}/{√19+√17}$

${19-17}/{√19+√17}=2/{√19+√17}$

Similarly,$√{13} -√{11}=2/{√{13} +√{11}}$

$√7 -√5=2/{√7 +√5}$

$√5-√3=2/{√5+√3}$

Clearly, $√5-√3$ is the greatest.

(Smaller the denominator, greater the no.)

Answer: (c)

$√2, √^3{9}, √^4{16}, √^5{32}$

$(16)^{1/4}=(2^4)^{1/4}=2$

$√^5{32}=(32)^{1/5}=(2^5)^{1/5}=2$

$√^3{9}>2,√2<2$

Answer: (a)

$√5 , 3√7 , 4√13$

$√5$

$3√7 =√{9×7}=√63$

$√^4{13}=√{4×4×13}=√{208}$

Clearly,$√5<3√7<4√13$