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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!

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What is the value of

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

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Heder Oliveira Dias**

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

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Patrick Engelmann**

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

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Rajen Kapur**

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

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

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Mehul Arora**

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

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

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Omkar Kulkarni**

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