a: \(=\sqrt{7}+1\)

b: \(=\sqrt{5}+\sqrt{2}\)

c: \(=\sqrt{5}-\sqrt{3}\)

d: \(=2\sqrt{3}-\sqrt{7}\)

a) \(-\sqrt[3]{81x^{10}y^5}=-\sqrt[3]{27\cdot x^9\cdot y^3\cdot3xy^2}=-3x^3y\cdot\sqrt[3]{3xy^2}.\)

b) \(\frac{\sqrt{80x^3}}{\sqrt{2x}}=\sqrt{\frac{80x^3}{2x}}=\sqrt{40x^2}=2\sqrt{10}x\)

\(a^2+2ab+b^2=\left(a+b\right)^2\ge0\forall a,b\)

\(a^2-2ab+b^2=\left(a-b\right)^2\ge0\forall a,b\)

\(A^{2n}\ge0\forall A\)

\(-A^{2n}\le0\forall A\)

\(\left|A\right|\ge0\forall A\)

\(-\left|A\right|\le0\forall A\)

\(\left|A\right|+\left|B\right|\ge\left|A+B\right|\)

\(\left|A\right|-\left|B\right|\le\left|A-B\right|\)

a/ \(\sqrt{10}< \sqrt{16}=4\)

b/ \(\sqrt{40}>\sqrt{36}=4\)

c/ \(\sqrt{15}+\sqrt{24}< \sqrt{16}+\sqrt{25}=4+5=9\)

d/ \(3\sqrt{2}=\sqrt{18}< \sqrt{20}=2\sqrt{5}\)

a) \(\sqrt{10}\)và 4
4 = \(\sqrt{16}\)
Do \(\sqrt{16}>\sqrt{10}\)nên \(4>\sqrt{10}\)
b) \(\sqrt{40}\)và 6
6 = \(\sqrt{36}\)
Do \(\sqrt{40}>\sqrt{36}\)nên\(\sqrt{40}>6\)
 

1)\(y=\dfrac{5}{7+\sqrt{x}}\le\dfrac{5}{7}\)

Dấu "=" xảy ra khi:

\(\sqrt{x}=0\Leftrightarrow x=0\)

b) \(y=\dfrac{\sqrt{x+1}+13}{\sqrt{x+1}+4}\le\dfrac{13}{4}\)

Dấu "=" xảy ra khi: \(\sqrt{x+1}=0\Leftrightarrow x=-1\)

2)\(\sqrt{x-1}+\sqrt{2x-2}+\sqrt{3x-3}+15\ge15\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\sqrt{x-1}=0\\\sqrt{2x-2}=0\\\sqrt{3x-3}=0\end{matrix}\right.\Leftrightarrow x=1\left(tm\right)\)