$\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$

makeupwn
2022-08-12
Answered

$\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$

You can still ask an expert for help

Hamza Conrad

Answered 2022-08-13
Author has **20** answers

$\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}=\frac{(\sqrt{7}+\sqrt{3})\times (\sqrt{7}+\sqrt{3})}{(\sqrt{7}-\sqrt{3})\times (\sqrt{7}+\sqrt{3})}$

$=\frac{7+3+2\sqrt{7}\sqrt{3}}{7-3}\phantom{\rule{0ex}{0ex}}=\frac{10+2\sqrt{21}}{4}\phantom{\rule{0ex}{0ex}}=\frac{5+\sqrt{21}}{2}$

$=\frac{7+3+2\sqrt{7}\sqrt{3}}{7-3}\phantom{\rule{0ex}{0ex}}=\frac{10+2\sqrt{21}}{4}\phantom{\rule{0ex}{0ex}}=\frac{5+\sqrt{21}}{2}$

asked 2022-06-03

Show there is a sequence of rational numbers converging to any irrational number.

asked 2022-06-27

Prove that the sum of a rational and irrational number is irrational.

asked 2022-07-07

Construct an increasing function $f$ on $R$ that is continuous at every irrational number and is discontinuous at every rational number.

Solution: Let ${r}_{n}$ be a sequence with distinct terms whose range is $\mathbb{Q}$. Let $f:\mathbb{R}\to \mathbb{R}$ be given by

$f(x)=\sum _{{r}_{n}<x}\frac{1}{{2}^{n}}$

Solution: Let ${r}_{n}$ be a sequence with distinct terms whose range is $\mathbb{Q}$. Let $f:\mathbb{R}\to \mathbb{R}$ be given by

$f(x)=\sum _{{r}_{n}<x}\frac{1}{{2}^{n}}$

asked 2022-07-06

Proving Is mth root of $2$ an irrational number for every integer $m\ge 2$

asked 2021-12-16

Whats the absolute value of $\frac{02}{}$ ?

asked 2022-05-20

Prove or disprove that there is a rational number $x$ and an irrational number $y$ such that ${x}^{y}$ is irrational.

asked 2022-06-16

Find a minimal polynomial of $\alpha $ when $\alpha $ is an irrational number satisfying ${\alpha}^{3}+3{\alpha}^{2}-2=0$.