The value of \(\sqrt{5+\sqrt[3]{59+\sqrt{21+\sqrt{13+\sqrt[3]{27}}}}}\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
A nested root is simplified from the innermost root outwards, each step giving a perfect square or cube for the next one.
Innermost cube root: \(\sqrt[3]{27}=3\)
Next square root: \(\sqrt{13+3}=\sqrt{16}=4\)
Next square root: \(\sqrt{21+4}=\sqrt{25}=5\)
The cube root: \(\sqrt[3]{59+5}=\sqrt[3]{64}=4\)
The outer square root: \(\sqrt{5+4}=\sqrt{9}=3\)