Question

9 Efectuati calculele: ​

Answer 1

a) $\frac{\sqrt{150}}{\sqrt{6}} =\sqrt{\frac{150}{6}} =\sqrt{25} =\sqrt{5^2} = 5$

b) $\frac{\sqrt{288}}{\sqrt{2}} =\sqrt{\frac{288}{2}} =\sqrt{144} =\sqrt{12^2} = 12$

c) $\frac{-\sqrt{147}}{\sqrt{3}} =-\frac{\sqrt{147}}{\sqrt{3}} =-\sqrt{\frac{147}{3}} =-\sqrt{49} = -7$

d) $\frac{\sqrt{294}}{\sqrt{6}} =\sqrt{\frac{294}{6}} =\sqrt{49} =\sqrt{7^2} = 7$

e) $\frac{\sqrt{10}-\sqrt{2}}{\sqrt{2}} =\frac{2\sqrt{5}-2}{2} =\frac{2\left(\sqrt{5}-1\right)}{2} =\sqrt{5}-1$

f) $\frac{3\sqrt{3}-\sqrt{6}}{\sqrt{3}} =\frac{\left(3\sqrt{3}-\sqrt{6}\right)\sqrt{3}}{\sqrt{3}\sqrt{3}} =\frac{9-3\sqrt{2}}{3} =\frac{3\left(3-\sqrt{2}\right)}{3} =3-\sqrt{2}$

g) $\frac{\sqrt{42}-\sqrt{7}}{\sqrt{7}} =\frac{\left(\sqrt{42}-\sqrt{7}\right)\sqrt{7}}{\sqrt{7}\sqrt{7}} =\frac{7\sqrt{6}-7}{7} =\frac{7\left(\sqrt{6}-1\right)}{7} =\sqrt{6}-1$

h) $\frac{\sqrt{63}+\sqrt{28}}{\sqrt{7}} =\frac{3\sqrt{7}+2\sqrt{7}}{\sqrt{7}} =\frac{5\sqrt{7}}{\sqrt{7}} =5$

i) $\frac{\sqrt{160}-\sqrt{250}}{\sqrt{10}} =\frac{4\sqrt{10}-5\sqrt{10}}{\sqrt{10}} \frac{-\sqrt{10}}{\sqrt{10}} =-\frac{\sqrt{10}}{\sqrt{10}}=-1$

j) $\frac{\sqrt{147}-\sqrt{108}}{\sqrt{3}} =\frac{7\sqrt{3}-6\sqrt{3}}{\sqrt{3}} =\frac{\sqrt{3}}{\sqrt{3}} = 1$

k) $\frac{\sqrt{320}-\sqrt{125}}{\sqrt{5}} =\frac{8\sqrt{5}-5\sqrt{5}}{\sqrt{5}} =\frac{3\sqrt{5}}{\sqrt{5}} =3$

l) $\frac{\sqrt{450}-\sqrt{150}}{\sqrt{5}} =\frac{15\sqrt{2}-5\sqrt{6}}{\sqrt{5}} =\frac{5\left(3\sqrt{2}-\sqrt{6}\right)}{\sqrt{5}}=\frac{5\left(3\sqrt{2}-\sqrt{6}\right)}{\sqrt{5}}$

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Succes!