Question

How would one prove that for all positive real $a$ and $b$, $\sqrt{a+b} \neq \sqrt{a} + \sqrt{b}$?

score 112 · Answer 1 · 2026-04-13 04:02:39

How would one prove that for all positive real $a$ and $b$, $\sqrt{a+b} \neq \sqrt{a} + \sqrt{b}$?

Published on 13 Apr 2026 - 4:02

score 178 · Answer 2 · 2026-04-13 14:09:13

How can I prove $\sqrt{5}$ is irrational using: for $n \in \mathbb{Z}$, $n^2 = 5a$ for some integer $a$ if and only if $n = 5b$ for some integer b$

score 110 · Answer 3 · 2026-03-26 19:17:17

110

Views

Suppose $a_1 , a_2 , \dots , a_n$ be positive. Consider sequences

Published on 26 Mar 2026 - 19:17

score 69 · Answer 4 · 2026-04-11 13:04:46

69

Views

Can someone tell me what should i do next? Should I use the inequality between Arithmetic and Geometric mean?

Published on 11 Apr 2026 - 13:04

score 162 · Answer 5 · 2026-04-11 10:44:13

162

Views

Range of radical function?

Published on 11 Apr 2026 - 10:44

score 360 · Answer 6 · 2026-04-10 00:29:50

360

Views

Integration of a square root of a reciprocal function

Published on 10 Apr 2026 - 0:29

score 1.3k · Answer 7 · 2026-04-12 09:00:24

1.3k

Views

Checking whether $5876432$ is a perfect square or not

Published on 12 Apr 2026 - 9:00

score 321 · Answer 8 · 2026-04-13 04:54:01

321

Views

How to solve higher index roots?

Published on 13 Apr 2026 - 4:54

score 76 · Answer 9 · 2026-04-01 11:04:46

76

Views

Solving $\int\sqrt{\sqrt{\left(\frac{1}{x+a}-\frac{1}{b}\right)}-\ln(x+a)-\frac{x}{b}+c} \, dx$ or $\int\sqrt{\ln(x+a)-\frac{x}{b}+c} \, dx$

Published on 01 Apr 2026 - 11:04

score 702 · Answer 10 · 2026-04-13 05:16:38

702

Views

Is the square of a square root always non-negative? ($\sqrt{x}^2 = |x|?$)

Published on 13 Apr 2026 - 5:16

score 64 · Answer 11 · 2026-04-10 16:30:46

64

Views

solving this radical equation; finding the value of q?

Published on 10 Apr 2026 - 16:30

score 44 · Answer 12 · 2026-04-09 04:47:57

44

Views

Finding the minima of a function in two ways

Published on 09 Apr 2026 - 4:47

score 172 · Answer 13 · 2026-04-13 09:31:52

172

Views

The group of real cube roots

Published on 13 Apr 2026 - 9:31

score 60 · Answer 14 · 2026-04-13 13:48:12

60

Views

How can I prove that $\sqrt{2} + \sqrt{3}$ is irrational using the fact that $\sqrt{2}$ is irrational?

Published on 13 Apr 2026 - 13:48

score 367 · Answer 15 · 2026-04-06 16:19:33

367

Views

If $x+iy=\sqrt\frac{1+i}{1-i}$, where $x$ and $y$ are real, prove that $x^2+y^2=1$

Published on 06 Apr 2026 - 16:19

List Question

How would one prove that for all positive real $a$ and $b$, $\sqrt{a+b} \neq \sqrt{a} + \sqrt{b}$?

How can I prove $\sqrt{5}$ is irrational using: for $n \in \mathbb{Z}$, $n^2 = 5a$ for some integer $a$ if and only if $n = 5b$ for some integer b$

Suppose $a_1 , a_2 , \dots , a_n$ be positive. Consider sequences

Can someone tell me what should i do next? Should I use the inequality between Arithmetic and Geometric mean?

Range of radical function?

Integration of a square root of a reciprocal function

Checking whether $5876432$ is a perfect square or not

How to solve higher index roots?

Solving $\int\sqrt{\sqrt{\left(\frac{1}{x+a}-\frac{1}{b}\right)}-\ln(x+a)-\frac{x}{b}+c} \, dx$ or $\int\sqrt{\ln(x+a)-\frac{x}{b}+c} \, dx$

Is the square of a square root always non-negative? ($\sqrt{x}^2 = |x|?$)

solving this radical equation; finding the value of q?

Finding the minima of a function in two ways

The group of real cube roots

How can I prove that $\sqrt{2} + \sqrt{3}$ is irrational using the fact that $\sqrt{2}$ is irrational?

If $x+iy=\sqrt\frac{1+i}{1-i}$, where $x$ and $y$ are real, prove that $x^2+y^2=1$

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