Simplify \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}}\)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7
A nested root is simplified from the innermost root outwards: each root is worked out and its value put into the root around it.
Innermost root: \(\sqrt{49}=7\), which leaves \(\sqrt{32-7}=\sqrt{25}=5\)
Next root: \(\sqrt{20+5}=\sqrt{25}=5\)
Outermost root: \(\sqrt{54-5}=\sqrt{49}=7\)