5) \(M=\dfrac{6}{2-\sqrt{3}}+\sqrt{\left(2-\sqrt{3}\right)^2}-\sqrt{75}=\dfrac{6\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+2-\sqrt{3}-5\sqrt{3}=12+6\sqrt{3}+2-\sqrt{3}-5\sqrt{3}=14\)6) \(\dfrac{2}{\sqrt{2}+2}+\dfrac{1}{3}.\sqrt{18}=\dfrac{2\left(\sqrt{2}-2\right)}{\left(\sqrt{2}+2\right)\left(\sqrt{2}-2\right)}+\dfrac{3\sqrt{2}}{3}=-\sqrt{2}+2+\sqrt{2}=2\)

7) \(P=\left(\dfrac{1}{2-\sqrt{3}}-\dfrac{1}{2+\sqrt{3}}\right).\dfrac{\sqrt{3}-1}{3-\sqrt{3}}=\dfrac{2+\sqrt{3}-2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}.\dfrac{\sqrt{3}-1}{\sqrt{3}\left(\sqrt{3}-1\right)}=2\sqrt{3}.\dfrac{1}{\sqrt{3}}=2\)8) \(A=\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}-\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}=\dfrac{\left(\sqrt{2+\sqrt{3}}\right)^2-\left(\sqrt{2-\sqrt{3}}\right)^2}{\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}}=\dfrac{2+\sqrt{3}-2+\sqrt{3}}{\sqrt{4-3}}=2\sqrt{3}\)

a) ĐKXĐ: \(\left\{{}\begin{matrix}x\ne2\\x\ne4\\x\ge0\end{matrix}\right.\)

A. Để các nhịp cẩu nở ra khi trời nắng nóng 

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

2) \(B=\dfrac{2}{\sqrt{7}-\sqrt{6}}-\sqrt{28}+\sqrt{54}=\dfrac{2\left(\sqrt{7}+\sqrt{6}\right)}{\left(\sqrt{7}-\sqrt{6}\right)\left(\sqrt{7}+\sqrt{6}\right)}-\sqrt{28}+\sqrt{54}=2\sqrt{7}+2\sqrt{6}-2\sqrt{7}+3\sqrt{6}=5\sqrt{6}\)3) \(A=\dfrac{4}{\sqrt{3}-1}-\dfrac{2}{\sqrt{2}+\sqrt{3}}-\sqrt{8}=\dfrac{4\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\dfrac{2\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}-\sqrt{8}=\dfrac{4\sqrt{3}+4}{2}-\dfrac{2\sqrt{2}-2\sqrt{3}}{-1}-2\sqrt{2}=2\sqrt{3}+2+2\sqrt{2}-2\sqrt{3}-2\sqrt{2}=2\)4) \(\dfrac{50-\sqrt{25}}{\sqrt{36}}=\dfrac{50-5}{6}=\dfrac{45}{6}=\dfrac{15}{2}\)

Cho mình sửa câu c lại dòng cuối nha:

\(\left(x+y-2-x-y\right)^2=\left(-2\right)^2=4\)

a) \(A=\left(5-x\right)\left(5+x\right)-x\left(4-x\right)-25=25-x^2-4x+x^2-25=-4x\)b) \(B=\left(x^2+1\right)\left(x+1\right)-\left(x+1\right)^3=\left(x+1\right)\left[x^2+1-\left(x+1\right)^2\right]=\left(x+1\right)\left(x^2+1-x^2-2x-1\right)=\left(x+1\right)\left(-2x\right)\)c) \(C=\left(x+y-2\right)^2-2\left(x+y-2\right)\left(y+x\right)+\left(x+y\right)^2=\left(x+y-1-x-y\right)^2=\left(-1\right)^2=1\)

\(\sqrt{x^3}+\sqrt{y^3}\left(đk:x,y\ge0\right)\)

\(=\left|x\right|\sqrt{x}+\left|y\right|\sqrt{y}=x\sqrt{x}+y\sqrt{y}\)

1) \(a^6+b^3=\left(a^2\right)^3+b^3=\left(a^2+b\right)\left(a^4-a^2b+b^2\right)\)

2) \(x^2-10x+25=\left(x-5\right)^2\)

3) \(8x^3-\dfrac{1}{8}=\left(2x\right)^3-\left(\dfrac{1}{3}\right)^3=\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2x}{3}+\dfrac{1}{4}\right)\)

4) \(x^2+4xy+4y^2=\left(x+2y\right)^2\)

\(\dfrac{\left|-5\right|7^4+7^3.25}{7^5.125-7^3.50}=\dfrac{5.7^3\left(7+5\right)}{7^3.5\left(25.7^2-10\right)}=\dfrac{12}{1215}=\dfrac{4}{405}\)

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