Đáp án:
a) $3$
b) $-3\sqrt 7$
c) $2$
Giải thích các bước giải:
a) $\sqrt{16}-\sqrt{(-3,5)^2}+\sqrt 2.\sqrt{\dfrac{25}{8}}$
$=4-|-3,5|+\sqrt 2.\dfrac{5}{2\sqrt 2}$
$=4-3,5+\dfrac{5}{2}$
$=3$
b) $\sqrt{(\sqrt 7-3)^2}-(\sqrt 7+1)^2+(\sqrt 2+\sqrt 7)(\sqrt 7-\sqrt 2)$
$=|\sqrt 7-3|-(7+2\sqrt 7+1)+(7-2)$
$=3-\sqrt 7-8-2\sqrt 7+5$
$=-3\sqrt 7$
c) $\sqrt{4-2\sqrt 3}+\dfrac{\sqrt{24+12\sqrt 3}}{\sqrt 2}$
$=\sqrt{3-2\sqrt 3+1}+\dfrac{\sqrt{24+2\sqrt{108}}}{\sqrt 2}$
$=\sqrt{(\sqrt 3-1)^2}+\dfrac{\sqrt{18+2.\sqrt{18}.\sqrt 6+6}}{\sqrt 2}$
$=|\sqrt 3-1|+\dfrac{\sqrt{(3\sqrt 2+\sqrt 6)^2}}{\sqrt 2}$
$=\sqrt 3-1+\dfrac{|3\sqrt 2-\sqrt 6|}{\sqrt 2}$
$=\sqrt 3-1+\dfrac{\sqrt 2.(3-\sqrt 3)}{\sqrt 2}$
$=\sqrt 3-1+3-\sqrt 3$
$=2$.
