Giải bài 5 trang 47

Đề bài

Tính

a) $\sqrt{\frac{16}{121}}$

b) $\sqrt{4\frac{21}{25}}$

c) $\sqrt{\frac{6,4}{8,1}}$

d) $\frac{\sqrt{300}}{\sqrt{27}}$

e) $\frac{\sqrt{6}}{\sqrt{150}}$

g) $\sqrt{\frac{3}{2}}:\sqrt{\frac{1}{24}}$

Lời giải chi tiết

a) $\sqrt{\frac{16}{121}}=\frac{\sqrt{16}}{\sqrt{121}}=\frac{\sqrt{4^2}}{\sqrt{{11}^2}}=\frac{4}{11}.$

b) $\sqrt{4\frac{21}{25}}=\sqrt{\frac{121}{25}}=\frac{\sqrt{{11}^2}}{\sqrt{5^2}}=\frac{11}{5}.$

c) $\sqrt{\frac{6,4}{8,1}}=\sqrt{\frac{64}{81}}=\frac{\sqrt{8^2}}{\sqrt{9^2}}=\frac{8}{9}$.

d) $\frac{\sqrt{300}}{\sqrt{27}}=\sqrt{\frac{300}{27}}=\sqrt{\frac{100}{9}}=\frac{\sqrt{{10}^2}}{\sqrt{3^2}}=\frac{10}{3}$ .

e) $\frac{\sqrt{6}}{\sqrt{150}}=\sqrt{\frac{6}{150}}=\sqrt{\frac{1}{25}}=\frac{1}{\sqrt{5^2}}=\frac{1}{5}$.

g) $\sqrt{\frac{3}{2}}:\sqrt{\frac{1}{24}}=\sqrt{\frac{3}{2}:\frac{1}{24}}=\sqrt{36}=\sqrt{6^2}=6$.