Maths Olympiad Prep

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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. Fractions can be typed as 3/2, and spacing doesn't matter.

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.

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