Question

Doprowadź do postaci aVb
.
​

Answer 1

a)

[tex]7\sqrt{5}+\sqrt{20}=7\sqrt{5}+\sqrt{4\cdot5}=7\sqrt{5}+2\sqrt{5}=9\sqrt{5}[/tex]

b)

[tex]\sqrt{48}-\sqrt{27}=\sqrt{16\cdot3}-\sqrt{9\cdot3}=4\sqrt{3}-3\sqrt{3}=\sqrt{3}[/tex]

c)

[tex]\sqrt{12}+\sqrt{75}=\sqrt{4\cdot3}+\sqrt{25\cdot3}=2\sqrt{3}+5\sqrt{3}=7\sqrt{3}[/tex]

d)

[tex]\sqrt{45}-\sqrt{125}=\sqrt{9\cdot5}-\sqrt{25\cdot5}=3\sqrt{5}-5\sqrt{5}=-2\sqrt{5}[/tex]

e)

[tex]0,2\sqrt{50}+0,8\sqrt{72}-0,3\sqrt{32}=0,2\sqrt{25\cdot2}+0,8\sqrt{36\cdot2}-0,3\sqrt{16\cdot2}=\\=0,2\cdot5\sqrt{2}+0,8\cdot6\sqrt{2}-0,3\cdot4\sqrt{2}=\sqrt{2}+4,8\sqrt{2}-1,2\sqrt{2}=4,6\sqrt{2}[/tex]

f)

[tex]3\sqrt{20}-\dfrac{1}{3}\sqrt{45}-5\sqrt{180}=3\sqrt{4\cdot5}-\dfrac{1}{3}\sqrt{9\cdot5}-5\sqrt{36\cdot5}=\\=3\cdot2\sqrt{5}-\dfrac{1}{3}\cdot3\sqrt{5}-5\cdot6\sqrt{5}=6\sqrt{5}-\sqrt{5}-30\sqrt{5}=-25\sqrt{5}[/tex]