What is the value of [3] 64 + [3] 125 [3] 27 ? - Vidyadip

MCQ

What is the value of $\frac{\sqrt[3]{64}+\sqrt[3]{125}}{\sqrt[3]{27}} ?$

A
2
✓
3
C
4
D
9

✓

Answer

Correct option: B.

3

(B) 3
By prime factorisation,
$64=2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\Rightarrow \sqrt[3]{64}=2 \times 2=4$
Now, by prime factorisation,
$125=5 \times 5 \times 5$
$\Rightarrow \sqrt[3]{125}=5$
Again, by prime factorisation,
$27=3 \times 3 \times 3$
$\Rightarrow \sqrt[3]{27}=3$
$\therefore \frac{\sqrt[3]{64}+\sqrt[3]{125}}{\sqrt[3]{27}}=\frac{4+5}{3}=\frac{9}{3}=3$

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