The greatest number among cube root of 2 , √3, cube root of 5 and 1.5 is

Question

The greatest number among \(\sqrt[3]{2} , \sqrt3,\sqrt[3]{5}\) and 1.5 is

(a) \(\sqrt[3]{2}\)

(b) \(\sqrt3\)

(c) \(\sqrt[3]{5}\)

(d) 1.5

Answer 1

(b) \(\sqrt3\)

LCM of 3 and 2 = 6

Given numbers are \(\sqrt[3]{2} , \sqrt3,\sqrt[3]{5}\) , 1.5 i.e,

2^1/3, 3^1/2, 5^1/3, 1.5 

∴ Raising each number to power 6, we get

(2^1/3)⁶, (3^1/2)⁶, (5^1/3)⁶, (1.5)⁶, 

i.e, 2², 3³, 5², \((\frac{3}{2})^6\)

i.e, 4, 27, 25, \(\frac{729}{64}.\)

Of all these numbers 27 is the greatest ⇒ \(\sqrt3\) is the greatest.