Question

C1. Tính:

a) \(\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)

b) \(\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)

C2. Tính

P = \(\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\) , \(a\ge0,b\ge0,a\ne b\)

Answer 1

Câu 2:

\( P = \dfrac{{a - b}}{{\sqrt a + \sqrt b }} + \dfrac{{a\sqrt a - b\sqrt b }}{{a + b + \sqrt {ab} }}\\ P = \dfrac{{\left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}{{\left( {\sqrt a + \sqrt b } \right)}} + \dfrac{{\left( {\sqrt a - \sqrt b } \right)\left( {a + \sqrt {ab} + b} \right)}}{{a + b + \sqrt {ab} }}\\ P= \sqrt a - \sqrt b + \sqrt a - \sqrt b \\ P = 2\sqrt a - 2\sqrt b \)

Answer 2

Câu 1:
\(a)\left( {3\sqrt {\dfrac{3}{5}} - \sqrt {\dfrac{5}{3}} + \sqrt 5 } \right)2\sqrt 5 + \dfrac{2}{3}\sqrt {75} \\ = 6\sqrt {\dfrac{{15}}{5}} - 2\sqrt {\dfrac{{25}}{3}} + 10 + \dfrac{{10\sqrt 3 }}{3}\\ = 6\sqrt 3 - \dfrac{{10}}{{\sqrt 3 }} + 10 + \dfrac{{10\sqrt 3 }}{3}\\ = 6\sqrt 3 - \dfrac{{10\sqrt 3 }}{3} + 10 + \dfrac{{10\sqrt 3 }}{3}\\ = 6\sqrt 3 + 10\\ b){\left( {\sqrt 3 - 1} \right)^2} - \sqrt {{{\left( {1 - \sqrt 3 } \right)}^2}} + \sqrt {{{\left( { - 3} \right)}^2}.3} \\ = 3 - 2\sqrt 3 + 1 - \sqrt 3 + 1 + \sqrt {{3^3}} \\ = 5 - 3\sqrt 3 + 3\sqrt 3 \\ = 5\)