Question

Bài 1 : So sánh

1) - 3 \(\sqrt{13}\) và -9

2) \(\sqrt{15}-1\) và \(\sqrt{10}\)

3)5 và \(\sqrt{8}+1\)

Answer 1

1) `-3\sqrt13=-3\sqrt13`

`-9=-3\sqrt9`

`\sqrt13>\sqrt9`

`=> -3\sqrt13 < -3\sqrt9`

`=> -3\sqrt13 < 9`.

2) `\sqrt15 < \sqrt16`

`<=> \sqrt15-1 < \sqrt16-1`

`<=> \sqrt15-1 < 3 < \sqrt10`

`=> \sqrt15-1 <\sqrt10`

3) `5=4+1=\sqrt16+1`

`\sqrt8+1=\sqrt8+1`

`=> 5>\sqrt8+1`

Answer 2

1) \(-3\sqrt{13}=-\sqrt{117}< -\sqrt{81}=-9\)

3) Ta có: \(5^2=25=9+16\)

\(\left(2\sqrt{2}+1\right)^2=9+4\sqrt{2}\)

mà \(16>4\sqrt{2}\)

nên \(5>2\sqrt{2}+1\)

Answer 3

1) $-3\sqrt{13}=-\sqrt{117}<-\sqrt{81}=-9$

3) Ta có: ${}^{}=25=9+16$

${}^{}=9+4\sqrt{2}$

mà $16>4\sqrt{2}$

nên $5>2\sqrt{2}+1$