Simplify \(\displaystyle\frac{\sqrt{81}+\sqrt[3]{64}}{\sqrt{3^3+4^2+\sqrt[3]{216}}}\)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{13}{7}\)
Work out each root separately, then simplify the expression under the large square root before taking that root.
Numerator: \(\sqrt{81}+\sqrt[3]{64}=9+4=13\)
Under the root in the denominator: \(3^3+4^2+\sqrt[3]{216}=27+16+6=49\)
Its square root gives the denominator: \(\sqrt{49}=7\)
Numerator over denominator: \(\displaystyle\frac{13}{7}\)