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

Answer: (b)

$√4, √^3{4}, √^4{6}$ and $√^6{8}$

$√3 =(3)^{1/2×6/6}=(3^6)^{1/12}=(729)^{1/12}$

$√^3{4}=(4)^{1/3×4/4}=(4^4)^{1/12}=(256)^{1/12}$

$√^4{6}=(6)^{1/4×3/3}=(6^3)^{1/12}=(216)^{1/12}$

$√^6{8}=(8)^{1/6×2/2}=(8^2)^{1/12}=(64)^{1/12}$

Now, it is clear that $√3$ is the greatest.

Answer: (a)

$3√2, 3√7, 6√5, 2√20$

$3√2=3×1.4=4.2$

$3√7=3×2.6=7.8$

$6√5=6×2.2=13.2$

$2√20=2×4.5=9$

Answer: (b)

LCM of 2, 3, 4, 3 = 12

Thus $√2 = (2^6)^{1/12}=√^12{64}$

$√^3{3} = (3^4)^{1/12}=√^12{81}$

$√^4{5} = √^12{5^3}=√^12{125}$

$√^3{2}=√^12{2^4}=√^12{16}$

Obviously, $√^4{5}$ is the greatest = 0.05

Answer: (a)

$√^3{2}$ or $√3$

$√^3{2} =2^{1/3}=2^{2/6}=√^6{4}$

$√{3} =3^{1/2}=3^{3/6}=√^6{27}$

Answer: (d)

$√2, √^3{3}, √^4{5}, √^6{6}$

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

$(2)^{1/2}=2^{6/12}=√^12{2^6}=√^12{64}$

$√^3{3}=√^12{3^4}=√^12{81}$

$√^4{5}=√^12{5^3}=√^12{125}$

$√^6{6}=√^12{6^2}=√^12{36}$

The greatest number = $√^4{5}$