What is the value of \(\sqrt{43+\sqrt{31+\sqrt{11+\sqrt{196}}}}\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7
Nested roots are worked from the innermost root outwards; each result is added to the number before it and the next root is taken.
\(\sqrt{196}=14\)
\(\sqrt{11+14}=\sqrt{25}=5\)
\(\sqrt{31+5}=\sqrt{36}=6\)
\(\sqrt{43+6}=\sqrt{49}=7\)