Issolvi (2sqrt{3}+3sqrt{5})*(2sqrt{3}-3sqrt{5})

$$(2 \sqrt{ 3 } +3 \sqrt{ 5 } ) \times (2 \sqrt{ 3 } -3 \sqrt{ 5 } )$$

Evalwa

$$-33$$

Passi tas-Soluzzjonijiet

Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(2\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}$$

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

$$2^{2}\left(\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$4\left(\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$4\times 3-\left(3\sqrt{5}\right)^{2}$$

Immultiplika 4 u 3 biex tikseb 12.

$$12-\left(3\sqrt{5}\right)^{2}$$

Espandi \left(3\sqrt{5}\right)^{2}.

$$12-3^{2}\left(\sqrt{5}\right)^{2}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$12-9\left(\sqrt{5}\right)^{2}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$12-9\times 5$$

Immultiplika 9 u 5 biex tikseb 45.

$$12-45$$

Naqqas 45 minn 12 biex tikseb -33.

$$-33$$

Fattur

$$-33$$