Rút gọn các biểu thức sau: 1/2 căn 48 - 2 căn 75 - căn 33/căn 11 + 5 căn 1 1/3

Giải Toán 9 Luyện tập: Rút gọn biểu thức căn bậc hai

Video Giải Bài 62 trang 33 Toán lớp 9 Tập 1

Bài 62 trang 33 Toán lớp 9 Tập 1:

a) $\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}$

b) $\sqrt{150}+\sqrt{1,6}.\sqrt{60}+4,5.\sqrt{2\frac{2}{3}}-\sqrt{6}$

c)  ($\sqrt{28}$ - 2$\sqrt{3}$ + $\sqrt{7}$). $\sqrt{7}$+ $\sqrt{84}$

d) ${\left(\sqrt{6}+\sqrt{5}\right)}^2-\sqrt{120}$

Lời giải:

a)

$\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}=\frac{1}{2}\sqrt{16.3}-2\sqrt{25.3}-\sqrt{\frac{33}{11}}+5\sqrt{\frac{4}{3}}=\frac{1}{2}\mathrm{.4.}\sqrt{3}-\mathrm{2.5.}\sqrt{3}-\sqrt{3}+5\frac{\sqrt{4}}{\sqrt{3}}=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\frac{\mathrm{5.2.}\sqrt{3}}{3}=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\frac{10}{3}\sqrt{3}=\left(2-10-1+\frac{10}{3}\right)\sqrt{3}=\frac{-17}{3}\sqrt{3}$

b)

$\sqrt{150}+\sqrt{1,6}.\sqrt{60}+4,5.\sqrt{2\frac{2}{3}}-\sqrt{6}=\sqrt{25.6}+\sqrt{1,6.60}+4,5.\sqrt{\frac{8}{3}}-\sqrt{6}=5\sqrt{6}+\sqrt{16.6}+4,5.\frac{1}{3}.\sqrt{3^2.\frac{4.2}{3}}-\sqrt{6}=5\sqrt{6}+4\sqrt{6}+3\sqrt{6}-\sqrt{6}=11\sqrt{6}$

c)

$\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right).\sqrt{7}+\sqrt{84}=\left(\sqrt{4.7}-2\sqrt{3}+\sqrt{7}\right).\sqrt{7}+\sqrt{4.21}=\left(2\sqrt{7}-2\sqrt{3}+\sqrt{7}\right).\sqrt{7}+2\sqrt{21}=\left(3\sqrt{7}-2\sqrt{3}\right).\sqrt{7}+2\sqrt{21}=3.7-2\sqrt{21}+2\sqrt{21}=21$

d)

${\left(\sqrt{6}+\sqrt{5}\right)}^2-\sqrt{120}={\left(\sqrt{6}\right)}^2+2.\sqrt{6}.\sqrt{5}+{\left(\sqrt{5}\right)}^2-\sqrt{4.30}=6+2\sqrt{30}+5-2\sqrt{30}=11$