Arrange {3},[3]{4},[4]{5} in ascending order.

Correct Answer is : 54,43,3[4]{5},[3]{4},{3}45,34,3

Correct Answer is : 54,43,3[4]{5},[3]{4},{3}45,34,3

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UPTET Paper 1 2022 Solved Paper

Question : 95 of 150

Marks: +1, -0

Arrange

\sqrt{3},\sqrt[3]{4},\sqrt[4]{5}

in ascending order.

Solution:

Concept:

To compare surds with different indices, convert them to a common exponent by using the LCM of the indices.

Explanation:

First, rewrite each surd as a power with the same denominator. The indices are 2, 3, and 4. Their LCM is 12.

\sqrt{3} = 3^{\frac{1}{2}} = 3^{\frac{6}{12}}

\sqrt[3]{4} = 4^{\frac{1}{3}} = 4^{\frac{4}{12}}

\sqrt[4]{5} = 5^{\frac{1}{4}} = 5^{\frac{3}{12}}

Now compare the bases inside the 12th root:

125 < 256 < 729

Thus,

\sqrt[4]{5} < \sqrt[3]{4} < \sqrt{3}

Answer:

\sqrt[4]{5},\sqrt[3]{4},\sqrt{3}

(Option C)

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