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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 1 Challenges

If $$a = \sqrt b$$ and $$a = 3$$, what is the value of $$b$$?

$\large \color{brown}5^{55} + \color{brown}5^{55} + \color{brown}5^{55} + \color{brown}5^{55} +\color{brown} 5^{55} = \ ?$

$\large \dfrac{ \color{green}2^{\color{blue}{5}}\times \color{green} 2^{\color{blue}{7}}}{\color{green} 2^{{\color{blue}{10}}}\times \color{green} 2^{\color{blue}{3}}}\times \color{purple}{3^0} = \ ?$

How many digits does the number $$1000^{ 1000 }$$ have?

Given that $$x$$ is a real number such that $$x^2-4x+4=0$$, find the value of $$x$$.

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