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

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

Evalwa

$$18\sqrt{6}+1\approx 45.09081537$$

Passi tas-Soluzzjonijiet

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

$$8\left(\sqrt{2}\right)^{2}+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

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

$$8\times 2+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

Immultiplika 8 u 2 biex tikseb 16.

$$16+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

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

$$16+20\sqrt{6}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

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

$$16+20\sqrt{6}-2\sqrt{6}-5\left(\sqrt{3}\right)^{2}$$

Ikkombina 20\sqrt{6} u -2\sqrt{6} biex tikseb 18\sqrt{6}.

$$16+18\sqrt{6}-5\left(\sqrt{3}\right)^{2}$$

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

$$16+18\sqrt{6}-5\times 3$$

Immultiplika -5 u 3 biex tikseb -15.

$$16+18\sqrt{6}-15$$

Naqqas 15 minn 16 biex tikseb 1.

$$1+18\sqrt{6}$$