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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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