Question

TYLKO JEDEN PRZYKŁAD KALSA 7
daje naj prosze o szybka pomoc

Answer 1

Odpowiedź:

[tex]\huge\boxed {~~\dfrac{1}{\sqrt{50} -\sqrt{8} } =\dfrac{\sqrt{2} }{6} ~~}[/tex]

Szczegółowe wyjaśnienie:

Korzystamy  ze wzor skróconego mnożenia:

• [tex](x-y)(x+y)=x^{2} -y^{2}[/tex]

oraz

• [tex]\sqrt[n]{x^{n}} =x^{n\cdot \frac{1}{n} } =x,~~zal.~~x\geq 0[/tex]

Obliczamy :

I. metoda

[tex]\dfrac{1}{\sqrt{50} -\sqrt{8} } \cdot \dfrac{\sqrt{50} +\sqrt{8} }{\sqrt{50} +\sqrt{8} } =\dfrac{\sqrt{25\cdot 2} +\sqrt{4\cdot 2} }{(\sqrt{50})^{2} -(\sqrt{8} )^{2}} =\dfrac{5\sqrt{2} +2\sqrt{2} }{50-8} =\dfrac{7\!\!\!\!\diagup^1\sqrt{2} }{42\!\!\!\!\!\diagup_6} =\dfrac{\sqrt{2} }{6}[/tex]

II. metoda

[tex]\sqrt{50} =\sqrt{25\cdot 2} =\sqrt{5^{2}\cdot 2} =5\sqrt{2} \\\\\sqrt{8} =\sqrt{4\cdot 2} =\sqrt{2^{2}\cdot 2} =2\sqrt{2} \\\\\dfrac{1}{\sqrt{50} -\sqrt{8} } =\dfrac{1}{5\sqrt{2} -2\sqrt{2} } =\dfrac{1}{3\sqrt{2} } \cdot \dfrac{\sqrt{2} }{\sqrt{2} } =\dfrac{\sqrt{2} }{6}[/tex]