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Algebra

Radical Expressions and Equations

Concept Quizzes

Radicals Warmup
Radical Equations Warmup
Simplifying Expressions with Radicals
Expressions with Exponents
Rationalizing Denominators
Multiple Radicals
Radical Equations
Infinitely Nested Radicals

Challenge Quizzes

Radical Expressions and Equations: Level 1 Challenges
Radical Expressions and Equations: Level 2 Challenges
Radical Expressions and Equations: Level 3 Challenges
Radical Expressions and Equations: Level 4 Challenges

Radical Expressions and Equations: Level 3 Challenges

$\LARGE \sqrt{3} - \sqrt{5}$

Which one of these choices is equivalent to the expression above?

\sqrt{8 + 2 \sqrt{15}}

\sqrt{5} - \sqrt{3}

\sqrt{8 - 2 \sqrt{15}}

none of these choices

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by Paul Ryan Longhas

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$\large \frac{4}{\big(\sqrt{5} + 1\big)\big(\sqrt[4]{5} + 1\big)\big(\sqrt[8]{5} + 1\big)\big(\sqrt[16]{5} + 1\big)}$

If the above expression is equal to $x$ , find the value of $(x+1)^{64}$ .

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by Matthew Kendall

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$\sqrt{3+\sqrt{3}+\sqrt{2+\sqrt{3}+\sqrt{7+\sqrt{48}}}} = a + \sqrt{b}$

If $a$ and $b$ are positive integers, find $a + b$ .

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by Rohit Udaiwal

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$\large \sqrt{4+\sqrt{4-\sqrt{ 4+\sqrt{4-\sqrt{ 4+\sqrt{4-\dots}}}}}}$

What is the closed form of the above expression?

x=\frac{1+\sqrt{15}}{2}

x=\frac{1+\sqrt{13}}{2}

x=\frac{1-\sqrt{15}}{2}

x=\frac{1-\sqrt{13}}{2}

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by A Former Brilliant Member

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The equation $x + \sqrt{x-2} = 4$ has $\text{\_\_\_\_\_\_\_\_\_\_}.$

2 real roots 1 real root 1 real and 1 imaginary root 2 imaginary roots

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by Soumo Mukherjee

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