Tất cả đều bằng nhau.

a: \(\dfrac{\sqrt{81}}{\sqrt{16}}=\dfrac{9}{4}=\dfrac{36}{16}< \dfrac{81}{16}\)

b: \(\sqrt{16+25}=\sqrt{41}< 9=\sqrt{16}+\sqrt{25}\)

\(\sqrt{\dfrac{25}{4}}-\sqrt{\dfrac{49}{16}}=\dfrac{5}{2}-\dfrac{7}{4}=\dfrac{10}{4}-\dfrac{7}{4}=\dfrac{3}{4}\)

căn 25/4-căn 49/16=căn(5/2)mũ 2-căn(7/4)mũ 2=5/2-7/4=3/4

\(5\sqrt{16}-4\sqrt{9}+\sqrt{25}-0,3\sqrt{400}\)

\(=20-12+5-6\)

\(=7\)

Ý của bạn là \(\left(5\sqrt{16}\right)-\left(4\sqrt{9}\right)+\left(\sqrt{25}\right)-\left(0,3\sqrt{400}\right)\)phải k???

\(\left(5\sqrt{16}\right)-\left(4\sqrt{9}\right)+\left(\sqrt{25}\right)-\left(0,3\sqrt{400}\right)\)

\(=\left(5.4\right)-\left(4.3\right)+5-\left(0,3.20\right)\\ =20-12+5-6\\ =8+5-6\\ =13-6\\ =7\)

Chúc các bạn học tốt

\(4-\sqrt{x^2+1}-2\sqrt{16\left(x^2+1\right)}+5\sqrt{25\left(x^2+1\right)}\)

\(=4-\sqrt{x^2+1}-4\sqrt{x^2+1}+25\sqrt{x^2+1}\)

\(=20\sqrt{x^2+1}+4\)

a) \(\sqrt[]{x^2-4x+4}=x+3\)

\(\Leftrightarrow\sqrt[]{\left(x-2\right)^2}=x+3\)

\(\Leftrightarrow\left|x-2\right|=x+3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=x+3\\x-2=-\left(x+3\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}0x=5\left(loại\right)\\x-2=-x-3\end{matrix}\right.\)

\(\Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\)

b) \(2x^2-\sqrt[]{9x^2-6x+1}=5\)

\(\Leftrightarrow2x^2-\sqrt[]{\left(3x-1\right)^2}=5\)

\(\Leftrightarrow2x^2-\left|3x-1\right|=5\)

\(\Leftrightarrow\left|3x-1\right|=2x^2-5\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2x^2-5\\3x-1=-2x^2+5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-4=0\left(1\right)\\2x^2+3x-6=0\left(2\right)\end{matrix}\right.\)

Giải pt (1)

\(\Delta=9+32=41>0\)

Pt \(\left(1\right)\) \(\Leftrightarrow x=\dfrac{3\pm\sqrt[]{41}}{4}\)

Giải pt (2)

\(\Delta=9+48=57>0\)

Pt \(\left(2\right)\) \(\Leftrightarrow x=\dfrac{-3\pm\sqrt[]{57}}{4}\)

Vậy nghiệm pt là \(\left[{}\begin{matrix}x=\dfrac{3\pm\sqrt[]{41}}{4}\\x=\dfrac{-3\pm\sqrt[]{57}}{4}\end{matrix}\right.\)

\(=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=\dfrac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+2\right)}{2+\sqrt{2}+\sqrt{3}}\)

=1+căn 2

\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{4}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=\dfrac{\left(\sqrt{2}+\sqrt{4}\right)+\left(\sqrt{6}+\sqrt{3}\right)+\left(\sqrt{4}+\sqrt{8}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=\dfrac{\sqrt{2}\left(1+\sqrt{2}\right)+\sqrt{3}\left(1+\sqrt{2}\right)+\sqrt{4}\left(1+\sqrt{2}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=\dfrac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(=1+\sqrt{2}\)