a) Ta có: \(A=\sqrt{23+6\sqrt{10}}-\sqrt{23-6\sqrt{10}}\)

\(=\sqrt{18+2\cdot3\sqrt{2}\cdot\sqrt{5}+5}-\sqrt{18-2\cdot3\sqrt{2}\cdot\sqrt{5}+5}\)

\(=\sqrt{\left(3\sqrt{2}+\sqrt{5}\right)^2}-\sqrt{\left(3\sqrt{2}-\sqrt{5}\right)^2}\)

\(=3\sqrt{2}+\sqrt{5}-3\sqrt{2}+\sqrt{5}\)

\(=2\sqrt{5}\)

b) Ta có: \(B=\left(\dfrac{2+\sqrt{2}}{\sqrt{2}+1}+1\right)\left(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}-1\right)\)

\(=\left(\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}+1\right)\left(\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}-1\right)\)

\(=\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)\)

=2-1=2

đây là toán lớp mấy vậy em

lowps 9-10

ể,toán lớp 1 á

\(\frac{23-2\sqrt{9}}{3}=\frac{23\sqrt{29.4}}{3}=\frac{23\sqrt{116}}{3}< \frac{23\sqrt{144}}{3}=\frac{23.12}{3}=92< 100=\sqrt{10}\)

Mà \(\sqrt{10}< \sqrt{27}\)nên \(\frac{23-2\sqrt{9}}{3}< \sqrt{27}\)

Vậy,...

\(A=\dfrac{1}{\sqrt{25}+\sqrt{24}}+\dfrac{1}{\sqrt{24}+\sqrt{23}}+....+\dfrac{1}{\sqrt{2}+1}\)

\(A=\sqrt{25}-\sqrt{24}+\sqrt{24}-\sqrt{23}+......+\sqrt{2}-1=\sqrt{25}-1=4\)

Số khá xấu. Bạn coi lại đề xem có viết nhầm biểu thức không?

- Đề sai nhiều vậy sửa lại đi bạn ;-;

e) Ta có: \(\sqrt{1-12x+36x^2}=5\)

\(\Leftrightarrow\left|6x-1\right|=5\)

\(\Leftrightarrow\left[{}\begin{matrix}6x-1=5\\6x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}6x=6\\6x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{2}{3}\end{matrix}\right.\)

Vậy: \(S=\left\{1;-\dfrac{2}{3}\right\}\)

\(a\)

\(\sqrt{7}+\sqrt{15}\) 

\(=\sqrt{7+15}\)

\(=4,69\)

\(4,69< 7\)

\(\Rightarrow\sqrt{7}+\sqrt{15}< 7\)

\(b\)

\(\sqrt{7}+\sqrt{15}+1\)

\(=\sqrt{7+15}+1\)

\(=4,69+1\)

\(=5,69\)

\(\sqrt{45}\)

\(=6,7\)

\(5,69< 6,7\)

\(\Rightarrow\)\(\sqrt{7}+\sqrt{15}+1\)\(< \)\(\sqrt{45}\)

\(c\)

\(\frac{23-2\sqrt{19}}{3}\)

\(=\frac{22.4,53}{3}\)

\(=\frac{95,7}{3}\)

\(=31,9\)

\(\sqrt{27}\)

\(=5,19\)

\(31,9>5,19\)

\(\text{​​}\Rightarrow\text{​​}\text{​​}\)\(\frac{23-2\sqrt{19}}{3}\)\(>\sqrt{27}\)

\(d\)

\(\sqrt{3\sqrt{2}}\)

\(=\sqrt{3.1,41}\)

\(=\sqrt{4,23}\)

\(=2,05\)

\(\sqrt{2\sqrt{3}}\)

\(=\sqrt{2.1,73}\)

\(=\sqrt{3,46}\)

\(=1,86\)

\(2,05>1,86\)

\(\Rightarrow\sqrt{3\sqrt{2}}>\sqrt{2\sqrt{3}}\)

\(Học \) \(Tốt !!!\)

a) Ta có : \(\sqrt{7}< \sqrt{9}=3;\sqrt{15}< \sqrt{16}=4\)

Do đó : \(\sqrt{7}+\sqrt{15}< 3+4=7\)

b) Ta có : \(\sqrt{17}>\sqrt{16}=4;\sqrt{5}>\sqrt{4}=2\)

\(\Rightarrow\sqrt{17}+\sqrt{5}+1>4+2+1=7\)

Lại có : \(\sqrt{45}< \sqrt{49}< 7\)

Do đó : \(\sqrt{17}+\sqrt{5}+1>\sqrt{45}\)

c) Ta thấy : \(\sqrt{19}>\sqrt{16}=4\)

\(\Rightarrow2\sqrt{19}>2.4=8\)

\(\Rightarrow-2\sqrt{19}< -8\)

\(\Rightarrow23-2\sqrt{19}< 23-8=15\)

\(\Rightarrow\frac{23-2\sqrt{19}}{3}< 5\). Mặt khác : \(\sqrt{27}>\sqrt{25}=5\)

Nên : \(\frac{23-2\sqrt{19}}{3}< \sqrt{27}\)

d) Vì : \(18>12>0\Rightarrow\sqrt{18}>\sqrt{12}>0\)

\(\Leftrightarrow3\sqrt{2}>2\sqrt{3}>0\)

\(\Rightarrow\sqrt{3\sqrt{2}}>\sqrt{2\sqrt{3}}\)

Đáp án B

1) 23 . 45 + 23 . 55 - 23

= 23 . (45 + 55 - 1)

= 23 . 99

= 2277

2) 2349 : 2¹ + {67 . 1³ + [23 + 45 - (45 + 2)]}

= 2349 : 2 + {67 . 1 + [68 - (45 + 2)]}

= 1174,5 + {67 + [68 - 47]}

= 1174,5 + {67 + 21}

= 1174,5 + 88

= 1262,5

3) 23 + 3 . 9 + 56

= 23 + 27 + 56

= 50 + 56

= 106

5) x - 34 = 235 - 30

x - 34 = 205

x        = 205 + 34

x        = 239