Maths Olympiad Prep

Library / /48 of 144

Algebra Difficulty 2.0 Junior Find the answer

Evaluate the expression 13+7+4\sqrt{13+\sqrt{7+\sqrt{4}}}.

A number or a short expression. Spacing and $ signs are ignored.

Solution

We evaluate from the inside towards the outside: 13+7+4=13+7+2=13+9=13+3=16=4\sqrt{13+\sqrt{7+\sqrt{4}}}=\sqrt{13+\sqrt{7+2}}=\sqrt{13+\sqrt{9}}=\sqrt{13+3}=\sqrt{16}=4.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.