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Algebra Warmups

From cracking cryptograms to calculating the top speed of a rocket, algebra gives you tools to apply mathematical reasoning to a wide range of problems. Dive in and see what you already know!

Algebra Warmups: Level 3 Challenges


What is the value of

\[ \large \sqrt{1\text{%}}\, ? \]

\[ \frac{100001+100003+100005+\cdots+199999}{1+3+5+7+\cdots+99999} = \ ? \]

Over all real numbers \(x\), find the minimum value of \( \sqrt{(x+6)^2+25} + \sqrt{(x-6)^2+121} \).

\[ \large (x+3)(x+4)(x+6)(x+7) = 1120 \]

Find the sum of all reals \(x\) satisfying the equation above.

\[\large \sqrt{-2}\times\sqrt{-3}=\ ?\]

In this problem, the square root is a function from the complex numbers to the complex numbers.


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