Question

Tính:

a) \(\sqrt{27}+\sqrt{75}-\sqrt{\dfrac{1}{3}}\)

b) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)

c) \(\dfrac{3}{\sqrt{7}+\sqrt{2}}+\dfrac{2}{3+\sqrt{7}}+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)

Answer 1

#Giải:

a)\(\sqrt{27}\)+\(\sqrt{75}\)-\(\sqrt{\dfrac{1}{3}}\)=8\(\sqrt{3}\)-\(\sqrt{\dfrac{1}{3}}\)=\(\dfrac{23\sqrt{3}}{3}\).

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

c)\(\dfrac{3}{\sqrt{7}+\sqrt{2}}\)+\(\dfrac{2}{3+\sqrt{7}}\)+\(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)=1,093+\(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)=2,507.

Answer 2

a) = \(3\sqrt{3}+5\sqrt{3}-\dfrac{1}{\sqrt{3}}\)

= \(3\sqrt{3}+5\sqrt{3}-\dfrac{3}{\sqrt{3}}\)

= \(\dfrac{23\sqrt{3}}{3}\)

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

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

= \(1+\sqrt{3}-\sqrt{3}+1\)

= 2

c) = \(\dfrac{3\left(\sqrt{7}-\sqrt{2}\right)}{5}+\dfrac{2\left(3-\sqrt{7}\right)}{2}+\left(2-\sqrt{2}\right)\left(\sqrt{2}+1\right)\)

= \(3\sqrt{7}-3\sqrt{2}+3-\sqrt{7}+2\sqrt{2}+2-2-\sqrt{2}\)

= \(\dfrac{3\sqrt{7}-3\sqrt{2}}{5}+3-\sqrt{7}+\sqrt{2}\)

= \(\dfrac{3\sqrt{7}-3\sqrt{2}-5\sqrt{7}+5\sqrt{2}}{5}+3\)

= \(\dfrac{-2\sqrt{7}+2\sqrt{2}}{5}+3\)

\(\approx2,5\)