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NCHMCT JEE 2025 Solved Paper

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Question : 1 of 200

Marks: +1, -0

Find the value of :

\frac{\sqrt[3]{3375}+\sqrt{144}}{\sqrt[3]{729}+\sqrt[3]{1728}}

$\frac{8}{7}$
$\frac{9}{7}$
$\frac{5}{4}$
$\frac{4}{3}$

Solution:

Concept:

Evaluate the cube roots and square root, then simplify the fraction.

Explanation:

\sqrt[3]{3375} = 15

and

\sqrt{144} = 12

, so numerator

= 15 + 12 = 27

.

\sqrt[3]{729} = 9

and

\sqrt[3]{1728} = 12

, so denominator

= 9 + 12 = 21

.

Therefore:

\frac{\sqrt[3]{3375}+\sqrt{144}}{\sqrt[3]{729}+\sqrt[3]{1728}} = \frac{27}{21} = \frac{9}{7}

Answer:

\frac{9}{7}

, i.e. option B.

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