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

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

Izrēķināt

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

Atrisinājuma darbības

Atbrīvojieties no iracionalitātes saucēju ar \frac{2\sqrt{3}}{2\sqrt{3}-3\sqrt{2}}, reizinot skaitītāju un saucēju ar 2\sqrt{3}+3\sqrt{2}.

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

Apsveriet \left(2\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+3\sqrt{2}\right). Reizināšanu var pārvērst par kvadrātu starpību, izmantojot šo kārtulu: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Aprēķiniet 2 pakāpē 2 un iegūstiet 4.

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

Skaitļa \sqrt{3} kvadrāts ir 3.

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

Reiziniet 4 un 3, lai iegūtu 12.

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

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

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

Aprēķiniet -3 pakāpē 2 un iegūstiet 9.

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

Skaitļa \sqrt{2} kvadrāts ir 2.

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

Reiziniet 9 un 2, lai iegūtu 18.

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

Atņemiet 18 no 12, lai iegūtu -6.

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

Daliet 2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right) ar -6, lai iegūtu -\frac{1}{3}\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right).

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

Izmantojiet distributīvo īpašību, lai reizinātu -\frac{1}{3}\sqrt{3} ar 2\sqrt{3}+3\sqrt{2}.

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

Reiziniet \sqrt{3} un \sqrt{3}, lai iegūtu 3.

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

Saīsiniet 3 un 3.

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

Saīsiniet 3 un 3.

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

Lai reiziniet \sqrt{3} un \sqrt{2}, reiziniet numurus zem kvadrātveida saknes.

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

Izmantojiet distributīvo īpašību, lai reizinātu 19 ar -2-\sqrt{6}.

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