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UPTET Paper 1 Model Test 2

Section: Mathematics

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Question : 94 of 150

Marks: +1, -0

Find the value of

\sqrt[3]{59+\sqrt{16+\sqrt[3]{722+\sqrt{49}}}}

6
2
8
4

Solution:

Concept:

Simplify nested radicals step-by-step from the innermost to the outermost using basic arithmetic and cube roots.

Explanation:

Start with the innermost part:

\sqrt{49}=7

.

Then inside the cube root:

722+7=729

. The cube root

\sqrt[3]{729}=9

because

9^3=729

.

Now

\sqrt{16+9}=\sqrt{25}=5

.

Then

59+5=64

. The cube root

\sqrt[3]{64}=4

because

4^3=64

.

Answer:

D. 4

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