Question

What does it mean to put $\sqrt{\phantom{-v}}$ alone below a square rooted expression?

score 117 · Answer 1 · 2026-04-13 05:18:45

117

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What does it mean to put $\sqrt{\phantom{-v}}$ alone below a square rooted expression?

Published on 13 Apr 2026 - 5:18

score 177 · Answer 2 · 2026-04-16 22:16:38

177

Views

If $a,b,c$ are rational numbers and if $\left(a+b\sqrt[3]{2}+c\sqrt[3]{4}\right)^3$ is also rational then prove that $ab+bc+ca=0$

Published on 16 Apr 2026 - 22:16

score 1.1k · Answer 3 · 2026-04-14 10:39:58

1.1k

Views

Sum of 2 positive irrational numbers is irrational?

Published on 14 Apr 2026 - 10:39

score 140 · Answer 4 · 2026-04-16 07:33:52

140

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There exist infinitely many primes of the form $p = \lfloor\sqrt{n} + \sqrt{n + 1}\rfloor$.

Published on 16 Apr 2026 - 7:33

score 68 · Answer 5 · 2026-04-13 02:32:58

68

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Floor of the power of a radical

Published on 13 Apr 2026 - 2:32

score 100 · Answer 6 · 2026-04-18 08:42:47

100

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if $a+b=2$, finding minimum value of $\frac{a^2+b^2}{\sqrt{a^2+1} \sqrt{b^2+4}}$

Published on 18 Apr 2026 - 8:42

score 422 · Answer 7 · 2026-04-15 11:24:12

422

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Solutions of $\sqrt{x^2+5x-14} + |x^2+4x-12|=0$

Published on 15 Apr 2026 - 11:24

score 119 · Answer 8 · 2026-04-15 06:24:38

119

Views

Solving $\sqrt{(\log_2x)^2 - 5|\log_2x| + 6} \le 2\sqrt{5}$

Published on 15 Apr 2026 - 6:24

score 113 · Answer 9 · 2026-04-16 03:32:34

113

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If $\sqrt{x^2} = \sqrt{16}$, then does $x= \pm\sqrt{16}$?

Published on 16 Apr 2026 - 3:32

score 204 · Answer 10 · 2026-04-17 03:00:35

204

Views

Solve $\sqrt{\frac{(2 - x)(2 - y)}{(2 + x)(2 + y)} + \frac{(2 - y)(2 - z)}{(2 + y)(2 + z)} + \frac{(2 - z)(2 - x)}{(2 + z)(2 + x)}}$

Published on 17 Apr 2026 - 3:00

score 186 · Answer 11 · 2026-03-26 02:53:59

186

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Comparing $\sqrt{5} + \sqrt{6} + \sqrt{11}$ and $8$ without calculating the values

Published on 26 Mar 2026 - 2:53

score 142 · Answer 12 · 2026-04-17 02:58:47

142

Views

Simplify $\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}} + \frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$

Published on 17 Apr 2026 - 2:58

score 48 · Answer 13 · 2026-04-15 01:31:23

48

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$\{\sqrt{x}\}+\{\sqrt{y}\}=1+\{\sqrt{z}\}$, defined as $\lfloor a\rfloor+\{a\}=a $

Published on 15 Apr 2026 - 1:31

score 68 · Answer 14 · 2026-04-16 18:56:18

68

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Exercise on limit of indeterminate form: $\lim_{x \rightarrow 1} \frac{\sqrt{x+3} - \sqrt{5-x}}{\sqrt{1+x} - \sqrt{2}} = \sqrt2$

Published on 16 Apr 2026 - 18:56

score 135 · Answer 15 · 2026-04-09 22:57:18

135

Views

simplify radicals

Published on 09 Apr 2026 - 22:57

List Question

What does it mean to put $\sqrt{\phantom{-v}}$ alone below a square rooted expression?

If $a,b,c$ are rational numbers and if $\left(a+b\sqrt[3]{2}+c\sqrt[3]{4}\right)^3$ is also rational then prove that $ab+bc+ca=0$

Sum of 2 positive irrational numbers is irrational?

There exist infinitely many primes of the form $p = \lfloor\sqrt{n} + \sqrt{n + 1}\rfloor$.

Floor of the power of a radical

if $a+b=2$, finding minimum value of $\frac{a^2+b^2}{\sqrt{a^2+1} \sqrt{b^2+4}}$

Solutions of $\sqrt{x^2+5x-14} + |x^2+4x-12|=0$

Solving $\sqrt{(\log_2x)^2 - 5|\log_2x| + 6} \le 2\sqrt{5}$

If $\sqrt{x^2} = \sqrt{16}$, then does $x= \pm\sqrt{16}$?

Solve $\sqrt{\frac{(2 - x)(2 - y)}{(2 + x)(2 + y)} + \frac{(2 - y)(2 - z)}{(2 + y)(2 + z)} + \frac{(2 - z)(2 - x)}{(2 + z)(2 + x)}}$

Comparing $\sqrt{5} + \sqrt{6} + \sqrt{11}$ and $8$ without calculating the values

Simplify $\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}} + \frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$

$\{\sqrt{x}\}+\{\sqrt{y}\}=1+\{\sqrt{z}\}$, defined as $\lfloor a\rfloor+\{a\}=a $

Exercise on limit of indeterminate form: $\lim_{x \rightarrow 1} \frac{\sqrt{x+3} - \sqrt{5-x}}{\sqrt{1+x} - \sqrt{2}} = \sqrt2$

simplify radicals

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