Question

* Tính giá trị của biểu thức:

a. A=\(2\sqrt{2}-3\sqrt{18}+4\sqrt{32}-\sqrt{50}\)

b. B=\(\sqrt{\left(1-\sqrt{5}\right)^2}+\sqrt{6+2\sqrt{5}}\)

c. C=\(\dfrac{1}{2-\sqrt{6}}+\dfrac{1}{2+\sqrt{6}}\)

Answer 1

\(a,A=2\sqrt{2}-9\sqrt{2}+16\sqrt{2}-5\sqrt{2}\)

\(=4\sqrt{2}\)

\(b,B=\left|1-\sqrt{5}\right|+\sqrt{5+2\sqrt{5}+1}\)

\(=\left|1-\sqrt{5}\right|+\sqrt{\left(\sqrt{5}+1\right)^2}\)

\(=\left|1-\sqrt{5}\right|+\left|\sqrt{5}+1\right|=\sqrt{5}-1+\sqrt{5}+1=2\sqrt{5}\)

\(c,C=\dfrac{2+\sqrt{6}+2-\sqrt{6}}{\left(2+\sqrt{6}\right)\left(2-\sqrt{6}\right)}=\dfrac{4}{4-6}=-2\)
 

Answer 2

Lời giải:

a. 

\(A=2\sqrt{2}-3\sqrt{18}+4\sqrt{32}-\sqrt{50}=2\sqrt{2}-9\sqrt{2}+16\sqrt{2}-5\sqrt{2}\)

\(=(2-9+16-5)\sqrt{2}=4\sqrt{2}\)

b.

\(B=\sqrt{(1-\sqrt{5})^2}+\sqrt{(\sqrt{5}+1)^2}=|1-\sqrt{5}|+|\sqrt{5}+1|=\sqrt{5}-1+\sqrt{5}+1=2\sqrt{5}\)

c.

\(C=\frac{2+\sqrt{6}+2-\sqrt{6}}{(2-\sqrt{6})(2+\sqrt{6})}=\frac{4}{2^2-6}=-2\)

Answer 3

`a)A=2sqrt2-3sqrt{18}+4sqrt{32}-sqrt{50}`

`=2sqrt2-3sqrt{9.2}+4sqrt{16.2}-sqrt{25.2}`

`=2sqrt2-9sqrt2+16sqrt2-5sqrt2`

`=4sqrt2`

`b)B=sqrt{(1-sqrt5)^2}+sqrt{6+2sqrt5}`

`=sqrt5-1+sqrt{(sqrt5+1)^2}`

`=sqrt5-1+sqrt5+1=2sqrt5`

`c)1/(2-sqrt6)+1/(2+sqrt6)`

`=(2+sqrt6)/(4-6)+(sqrt6-2)/(6-4)`

`=(sqrt6-2-sqrt6-2)/2=-2`