Decimals and Fractions Practice Test 2

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Question : 35 of 40

Marks: +1, -0

From among

2^{1/2},3^{1/3},8^{1/8}

and

9^{1/9}

, the greatest is

$2^{1/2}$
$3^{1/3}$
$8^{1/8}$
$9^{1/9}$

Solution:

2^{1/2},3^{1/3},8^{1/8}

and

9^{1/9}

LCM of powers denominator, i.e., 2, 3, 8, 9 is 72

2^36,3^24,8^9,9^8

2^36,3^24, ((2)^3)^9, ((3)^2)^8

2^36,3^24,2^27,3^16

Clearly,

2^36 > 2^27\or 3^24 > 3^16

So,

2^36, 3^24⇒3^24 >2^36

From among

2^{1/2},3^{1/3},8^{1/8}

and

9^{1/9}

, the greatest is equal to

3^{1/3}.

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