zad.1
zapisz wyrażenie √2(√48 - √27 + √75) w postaci a√b
zad.2
uprość ułamek √12 + √75 kreska ułamkowa √3
zad.3 wykonaj działania (4 - 2√5)(√5 + 3)

[tex]\sqrt2(\sqrt{48}-\sqrt{27}+\sqrt{75})=\sqrt2(\sqrt{16\cdot3}-\sqrt{9\cdot3}+\sqrt{25\cdot3})=\\\\=\sqrt2(\sqrt{4^2\cdot3}-\sqrt{3^2\cdot3}+\sqrt{5^2\cdot3})=\sqrt2(4\sqrt3-3\sqrt3+5\sqrt3)=\\\\=\sqrt2(\sqrt3+5\sqrt3)=\sqrt2\cdot6\sqrt3=6\sqrt{2\cdot3}=\boxed{6\sqrt6}[/tex]

Zadanie 2

[tex]\frac{\sqrt{12}+\sqrt{75}}{\sqrt3}=\frac{\sqrt{4\cdot3}+\sqrt{25\cdot3}}{\sqrt3}=\frac{\sqrt{2^2\cdot3}+\sqrt{5^2\cdot3}}{\sqrt3}=\frac{2\sqrt3+5\sqrt3}{\sqrt3}=\frac{7\sqrt3}{\sqrt3}=\boxed7\\[/tex]

Zadanie 3

[tex](4-2\sqrt5)(\sqrt5+3)=4\cdot\sqrt5+4\cdot3-2\sqrt{5^2}-2\sqrt5\cdot3=\\\\=4\sqrt5+12-2\cdot5-6\sqrt5=4\sqrt5+12-10-6\sqrt5=\boxed{2-2\sqrt5}[/tex]

Mutopompkaviz Mutopompkaviz · Answer 2

Odpowiedź i szczegółowe wyjaśnienie:

ZADANIE 1:

[tex]\sqrt2(\sqrt{48}-\sqrt{27}+\sqrt{75})=\sqrt2(\sqrt{16\cdot3}-\sqrt{9\cdot3}+\sqrt{25\cdot3})=\\\\=\sqrt2(4\sqrt3-3\sqrt3+5\sqrt3)=\sqrt2\cdot6\sqrt3=6\sqrt{2\cdot3}=6\sqrt6[/tex]

ZADANIE 2.

[tex]\dfrac{\sqrt{12}+\sqrt{75}}{\sqrt3}=\dfrac{\sqrt{4\cdot3}+\sqrt{25\cdot3}}{\sqrt3}=\dfrac{2\sqrt3+5\sqrt3}{\sqrt3}=\dfrac{7\sqrt3}{\sqrt3}=7[/tex]

ZADANIE 3.

[tex](4-2\sqrt5)(\sqrt5+3)=4\cdot\sqrt5+4\cdot3-2\sqrt5\cdot\sqrt5-2\sqrt5\cdot3=\\\\=4\sqrt5+12-2\cdot5-6\sqrt5=-2\sqrt5+12-10=2-2\sqrt5[/tex]