Issolvi (4sqrt{2}-2sqrt{3})(2sqrt{3}+5sqrt{2})

$$( 4 \sqrt { 2 } - 2 \sqrt { 3 } ) ( 2 \sqrt { 3 } + 5 \sqrt { 2 } )$$

Evalwa

$$28-2\sqrt{6}\approx 23.101020514$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 4\sqrt{2}-2\sqrt{3} b'kull terminu ta' 2\sqrt{3}+5\sqrt{2}.

$$8\sqrt{3}\sqrt{2}+20\left(\sqrt{2}\right)^{2}-4\left(\sqrt{3}\right)^{2}-10\sqrt{3}\sqrt{2}$$

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

$$8\sqrt{6}+20\left(\sqrt{2}\right)^{2}-4\left(\sqrt{3}\right)^{2}-10\sqrt{3}\sqrt{2}$$

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

$$8\sqrt{6}+20\times 2-4\left(\sqrt{3}\right)^{2}-10\sqrt{3}\sqrt{2}$$

Immultiplika 20 u 2 biex tikseb 40.

$$8\sqrt{6}+40-4\left(\sqrt{3}\right)^{2}-10\sqrt{3}\sqrt{2}$$

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

$$8\sqrt{6}+40-4\times 3-10\sqrt{3}\sqrt{2}$$

Immultiplika -4 u 3 biex tikseb -12.

$$8\sqrt{6}+40-12-10\sqrt{3}\sqrt{2}$$

Naqqas 12 minn 40 biex tikseb 28.

$$8\sqrt{6}+28-10\sqrt{3}\sqrt{2}$$

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

$$8\sqrt{6}+28-10\sqrt{6}$$

Ikkombina 8\sqrt{6} u -10\sqrt{6} biex tikseb -2\sqrt{6}.

$$-2\sqrt{6}+28$$

Fattur

$$2 {(14 - \sqrt{6})} = 23.101020514$$