Rešite 19frac{2sqrt{3}}{2sqrt{3}-3sqrt{2}}

$$19 \frac { 2 \sqrt { 3 } } { 2 \sqrt { 3 } - 3 \sqrt { 2 } }$$

Ovrednoti

$$-19\sqrt{6}-38\approx -84,540305113$$

Koraki rešitve

Racionalizirajte imenovalec \frac{2\sqrt{3}}{2\sqrt{3}-3\sqrt{2}} tako, da pomnožite števec in imenovalec s 2\sqrt{3}+3\sqrt{2}.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{\left(2\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+3\sqrt{2}\right)}$$

Razmislite o \left(2\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+3\sqrt{2}\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{\left(2\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}$$

Razčlenite \left(2\sqrt{3}\right)^{2}.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{2^{2}\left(\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}$$

Izračunajte potenco 2 števila 2, da dobite 4.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{4\left(\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}$$

Kvadrat vrednosti \sqrt{3} je 3.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{4\times 3-\left(-3\sqrt{2}\right)^{2}}$$

Pomnožite 4 in 3, da dobite 12.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-\left(-3\sqrt{2}\right)^{2}}$$

Razčlenite \left(-3\sqrt{2}\right)^{2}.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-\left(-3\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Izračunajte potenco -3 števila 2, da dobite 9.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-9\left(\sqrt{2}\right)^{2}}$$

Kvadrat vrednosti \sqrt{2} je 2.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-9\times 2}$$

Pomnožite 9 in 2, da dobite 18.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-18}$$

Odštejte 18 od 12, da dobite -6.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{-6}$$

Delite 2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right) s/z -6, da dobite -\frac{1}{3}\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right).

$$19\left(-\frac{1}{3}\right)\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)$$

Uporabite distributivnost, da pomnožite -\frac{1}{3}\sqrt{3} s/z 2\sqrt{3}+3\sqrt{2}.

$$19\left(-\frac{1}{3}\sqrt{3}\times 2\sqrt{3}-\frac{1}{3}\sqrt{3}\times 3\sqrt{2}\right)$$

Pomnožite \sqrt{3} in \sqrt{3}, da dobite 3.

$$19\left(-\frac{1}{3}\times 3\times 2-\frac{1}{3}\sqrt{3}\times 3\sqrt{2}\right)$$

Okrajšaj 3 in 3.

$$19\left(-2-\frac{1}{3}\sqrt{3}\times 3\sqrt{2}\right)$$

Okrajšaj 3 in 3.

$$19\left(-2-\sqrt{3}\sqrt{2}\right)$$

Če želite \sqrt{3} pomnožite in \sqrt{2}, pomnožite številke v kvadratni korenu.

$$19\left(-2-\sqrt{6}\right)$$

Uporabite distributivnost, da pomnožite 19 s/z -2-\sqrt{6}.

$$-38-19\sqrt{6}$$