## Euclid 2022 Question 1, CEMC UWaterloo

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#### Difficulty: 4

#### This problem is tagged with euclid, euclid22, highschool.

**(Euclid 2022, Question 1, CEMC - UWaterloo)**

(a) What is the value of $\frac{3^2 − 2^3}{2^3 − 3^2}$ ?

(b) What is the value of $\sqrt{\sqrt{81} + \sqrt{9} − \sqrt{64}}$ ?

(c) Determine all real numbers $x$ for which $\frac{1}{\sqrt{x^2 + 7}}=\frac{1}{4}$.

*Answer Submission Note(s)*

In part (c), sort your answers in ascending order and separate them with a comma.

Separate the answers for each part with a single space.

For example: "a b c1,c2"

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