Issolvi (3sqrt{2}+2sqrt{3})(3sqrt{2}-4sqrt{3})

$$( 3 \sqrt { 2 } + 2 \sqrt { 3 } ) ( 3 \sqrt { 2 } - 4 \sqrt { 3 } )$$

Evalwa

$$-6\sqrt{6}-6\approx -20.696938457$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 3\sqrt{2}+2\sqrt{3} b'kull terminu ta' 3\sqrt{2}-4\sqrt{3}.

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$9\times 2-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Immultiplika 9 u 2 biex tikseb 18.

$$18-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Biex timmultiplika \sqrt{3} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$18-12\sqrt{6}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Biex timmultiplika \sqrt{3} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$18-12\sqrt{6}+6\sqrt{6}-8\left(\sqrt{3}\right)^{2}$$

Ikkombina -12\sqrt{6} u 6\sqrt{6} biex tikseb -6\sqrt{6}.

$$18-6\sqrt{6}-8\left(\sqrt{3}\right)^{2}$$

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

$$18-6\sqrt{6}-8\times 3$$

Immultiplika -8 u 3 biex tikseb -24.

$$18-6\sqrt{6}-24$$

Naqqas 24 minn 18 biex tikseb -6.

$$-6-6\sqrt{6}$$

Fattur

$$6 {(-\sqrt{6} - 1)} = -20.696938457$$