List questions from radicals

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What should the initial guess be for the Babylonian method of calculating square roots?

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Let $A_n=\frac{(n+1)+(n+2)+(n+3)+.....+(n+n)}{n}$,$B_n=[(n+1)(n+2)(n+3)....(n+n)]^{1/n}$.If $\lim_{n\to\infty}\frac{A_n}{B_n}=\frac{ae}{b}$

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Rationalization of a fraction

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Prove that $\sqrt{3}$ is not a rational number

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Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?

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Computing $\sqrt[3]{1\,}$

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Simplifying Cube Roots Containing a Square Root

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cyclic three variable inequality

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Prove the existence of the square root of $2$.

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Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$

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Limit $\lim_{x \to \infty} \frac{\sqrt{x^2 -1}}{2x+1}$

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Prove that $ \lim_\limits{x \to \infty} x(\sqrt{x^2+1}-x) $ = $ \frac{1}{2}$?

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Why is $\sqrt{x^2} = |x|$?

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If $\sqrt{28x}$ is an integer is $\sqrt{7x}$ always an integer?

Published on 03 Sep 2015 - 23:19

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Evaluating Continued Product of Radicals

What should the initial guess be for the Babylonian method of calculating square roots?

Let $A_n=\frac{(n+1)+(n+2)+(n+3)+.....+(n+n)}{n}$,$B_n=[(n+1)(n+2)(n+3)....(n+n)]^{1/n}$.If $\lim_{n\to\infty}\frac{A_n}{B_n}=\frac{ae}{b}$

Rationalization of a fraction

Prove that $\sqrt{3}$ is not a rational number

Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?

Computing $\sqrt[3]{1\,}$

Simplifying Cube Roots Containing a Square Root

cyclic three variable inequality

Prove the existence of the square root of $2$.

Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$

Limit $\lim_{x \to \infty} \frac{\sqrt{x^2 -1}}{2x+1}$

Prove that $ \lim_\limits{x \to \infty} x(\sqrt{x^2+1}-x) $ = $ \frac{1}{2}$?

Why is $\sqrt{x^2} = |x|$?

If $\sqrt{28x}$ is an integer is $\sqrt{7x}$ always an integer?

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