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Infinite nested radical with variables

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#linear-algebra #radicals #nested-radicals
50
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Can I sum summands within square root?

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#radicals
825
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Definition or proof of $a^{\frac mn}=\sqrt[n]{a^m}$?

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#algebra-precalculus #proof-writing #radicals
164
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Let $a$ and $b$ be positive integers such that $(\sqrt[3]{a} + \sqrt[3]{b} - 1)^2 = 49 + 20 \sqrt[3]{6}.$ Find $a + b.$

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#polynomials #radicals
192
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What is the real cube root of $3^{3^{333}}$?

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#arithmetic #radicals
70
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Prove that for $a,b,x \in \mathbb R_+$ and $a,b \ge 1$, then $a<b \implies a^x < b^x$.

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#real-analysis #real-numbers #radicals #supremum-and-infimum
68
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Number Theory Equality of Radicals

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#arithmetic #radicals
186
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$a_{n+1} = \sqrt{2 + a_n}$ Specific Theorem Needed

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#real-analysis #continuity #radicals
1.7k
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Fixed point iteration for cube root

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#numerical-methods #roots #radicals #fixed-point-theorems
44
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How to show that a particular sequence is always above a certain value?

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#real-analysis #sequences-and-series #recurrence-relations #radicals
311
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Solving for $x$ and $y$ when $(3x + y)(x + 3y)\sqrt{xy} = 14$

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#systems-of-equations #radicals #symmetric-functions
40
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How to simplify surd expressions such as this?

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#radicals
69
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Finding $x$ when $\sqrt{3x - 4} + \sqrt[3]{5 - 3x} = 1$

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#radicals
10.5k
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Elementary solution to $ \int \frac{1}{x^5+1} \, dx $

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#integration #indefinite-integrals #radicals #partial-fractions
38
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Previously adding restrictions

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#algebra-precalculus #logarithms #exponentiation #radicals

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