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Radical Expressions and Equations

Radical Expressions and Equations: Level 3 Challenges


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

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

4(5+1)(54+1)(58+1)(516+1)\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 xx, find the value of (x+1)64 (x+1)^{64} .

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

If aa and bb are positive integers, find a+b a + b .

4+44+44+4 \large \sqrt{4+\sqrt{4-\sqrt{ 4+\sqrt{4-\sqrt{ 4+\sqrt{4-\dots}}}}}}

What is the closed form of the above expression?

The equation x+x2=4 x + \sqrt{x-2} = 4 has __________.\text{\_\_\_\_\_\_\_\_\_\_}.


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