The greatest among the following numbers of 3¹/3}, 2¹/2}, 1, 6¹/6} is:

Correct Answer is : 3133¹/3}331

Correct Answer is : 3133¹/3}331

Test Index

Problems based on Numbers Test 1

Question : 4 of 40

Marks: +1, -0

3^{\frac{1}{3}}, 2^{\frac{1}{2}}, 1, 6^{\frac{1}{6}}

is:

Solution: 👈: Video Solution

Concept:

To compare numbers with different roots, make their powers equal using the LCM of the root indices.

Explanation:

The given numbers are

3^{\frac{1}{3}}, 2^{\frac{1}{2}}, 1,

and

6^{\frac{1}{6}}

LCM of

3, 2,

and

6

6

Raise each number to the power

6

(3^{\frac{1}{3}})^6 = 3^2 = 9

(2^{\frac{1}{2}})^6 = 2^3 = 8

1^6 = 1

(6^{\frac{1}{6}})^6 = 6

Since

9 > 8 > 6 > 1

, the greatest number is

3^{\frac{1}{3}}

Answer:

3^{\frac{1}{3}}

Go to Question:

Prev Question

Next Question