Evaluate:

Question:

Evaluate: $\sqrt[3]{4096}$

Solution:

$\sqrt[3]{4096}$

By prime factorisation method:

$\sqrt[3]{4096}=\sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}=\sqrt[3]{(2)^{3} \times(2)^{3} \times(2)^{3} \times(2)^{3}}$

$\sqrt[3]{4096}=(2) \times(2) \times(2) \times(2)=16$

$\therefore \sqrt[3]{4096}=16$

 

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