Em kéo xuống trang 40, mục số 3:

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\(\frac{7}{13}.\frac{5}{19}+\frac{7}{19}.\frac{8}{13}-3\frac{7}{19}\)

\(=\frac{7}{19}.\frac{5}{13}+\frac{7}{19}.\frac{8}{13}-3-\frac{7}{19}\)

\(=\frac{7}{19}\left(\frac{5}{13}+\frac{8}{13}\right)-3-\frac{7}{19}\)

\(=\frac{7}{19}-3-\frac{7}{19}\)

\(=-3\)

\(\frac{7}{13}.\frac{5}{19}+\frac{7}{19}.\frac{8}{13}-3\frac{7}{19}\)  

=\(\frac{7}{19}.\frac{5}{13}+\frac{7}{19}.\frac{8}{13}-3-\frac{7}{19}\)

= \(\frac{7}{19}.\left(\frac{5}{13}+\frac{8}{13}\right)-3-\frac{7}{19}\)

= \(\frac{7}{19}-3-\frac{7}{19}\) =  \(-3\)

\(\left|2\sqrt{3}-4\right|-\sqrt{\left(\sqrt{16}-\sqrt{3}\right)^2}=4-2\sqrt{3}-\left|\sqrt{16}-\sqrt{3}\right|=4-2\sqrt{3}-4+\sqrt{3}=-\sqrt{3}\)

rút rút gọn

\(\sqrt{19-8\sqrt{3}}\)

\(= \sqrt{16-8\sqrt{3}+3}\)

\(=\sqrt{(4-\sqrt{3})^2}\)

\(=\)\(|4-\sqrt{3}|\)

\(=4-\sqrt{3}\)

1) \(\left(\sqrt{19}-3\right)\left(\sqrt{19}+3\right)=\left(\sqrt{19}\right)^2-3^2=19-9=10\)

2) \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}=\sqrt{\dfrac{8+2\sqrt{7}}{2}}-\sqrt{\dfrac{8-2\sqrt{7}}{2}}\)

\(=\sqrt{\dfrac{\left(\sqrt{7}\right)^2+2.\sqrt{7}.1+1^2}{2}}-\sqrt{\dfrac{\left(\sqrt{7}\right)^2-2.\sqrt{7}.1+1^2}{2}}\)

\(=\sqrt{\dfrac{\left(\sqrt{7}+1\right)^2}{2}}-\sqrt{\dfrac{\left(\sqrt{7}-1\right)^2}{2}}=\dfrac{\left|\sqrt{7}+1\right|}{\sqrt{2}}-\dfrac{\left|\sqrt{7}-1\right|}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7}+1}{\sqrt{2}}-\dfrac{\sqrt{7}-1}{\sqrt{2}}=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)

3) \(\sqrt{8+\sqrt{60}}+\sqrt{45}-\sqrt{12}=\sqrt{8+\sqrt{4.15}}+\sqrt{9.5}-\sqrt{4.3}\)

\(=\sqrt{8+2\sqrt{15}}+3\sqrt{5}-2\sqrt{3}\)

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

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

\(\sqrt{5}+\sqrt{3}+3\sqrt{5}-2\sqrt{3}=4\sqrt{5}-\sqrt{3}\)

4) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)

\(=\sqrt{\left(\sqrt{5}\right)^2-2.2.\sqrt{5}+2^2}-\sqrt{\left(\sqrt{5}\right)^2+2.2.\sqrt{5}+2^2}\)

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

\(=\sqrt{5}-2-\sqrt{5}-2=-4\)

1) \(\left(\sqrt{19}-3\right)\left(\sqrt{19}+3\right)=19-9=10\)

4) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}=\sqrt{5}-2-\sqrt{5}-2=-4\)

\(\sqrt{12-6\sqrt{3}}=\sqrt{9-6\sqrt{3}+3}=\sqrt{3^2-2.3.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(3-\sqrt{3}\right)^2}\)

\(=\left|3-\sqrt{3}\right|=3-\sqrt{3}\)

\(\sqrt{19+8\sqrt{3}}=\sqrt{16+8\sqrt{3}+3}=\sqrt{4^2+2.4.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(4+\sqrt{3}\right)^2}\)

\(=\left|4+\sqrt{3}\right|=4+\sqrt{3}\)

\(\sqrt{14-6\sqrt{5}}=\sqrt{9-6\sqrt{5}+5}=\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(3-\sqrt{5}\right)^2}\)

\(=\left|3-\sqrt{5}\right|=3-\sqrt{5}\)

\(\sqrt{12-6\sqrt{3}}=\sqrt{3^2-2.3.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(3-\sqrt{3}\right)^2}=\left|3-\sqrt{3}\right|=3-\sqrt{3}\)

\(\sqrt{19+8\sqrt{3}}=\sqrt{4^2+2.4.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(4+\sqrt{3}\right)^2}=\left|4+\sqrt{3}\right|=4+\sqrt{3}\)

\(\sqrt{14-6\sqrt{5}}=\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(3-\sqrt{5}\right)^2}=\left|3-\sqrt{5}\right|=3-\sqrt{5}\)

\(\sqrt{12-6\sqrt{3}}=3-\sqrt{3}\)

\(\sqrt{19+8\sqrt{3}}=4+\sqrt{3}\)

\(\sqrt{14-6\sqrt{5}}=3-\sqrt{5}\)

\(\sqrt{9+2\sqrt{8}}\)thì được

\(\sqrt{9+8\sqrt{2}}\)

\(=\sqrt{9+2\sqrt{8}}\)

=\(\sqrt{8+2\sqrt{8}+1}\)

\(=\sqrt{\left(\sqrt{8}+1\right)^2}\)

\(=\sqrt{8}+1\)

\(\frac{\sqrt{x}+2}{\sqrt{x}-5}=\frac{\sqrt{x}-5+7}{\sqrt{x}-5}=1+\frac{7}{\sqrt{x}-5}\)

\(=\frac{\left(\sqrt{x}-5\right)+7}{\sqrt{x}-5}=1+\frac{7}{\sqrt{x}-5}\)

Em nghĩ thế thôi chứ sai đúng em ko biết đâu nha 

ukm le tai bao chau 

em làm dúng òi rá

hok tốt