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

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

Evalwa

$$4-9\sqrt{6}\approx -18.045407685$$

Passi tas-Soluzzjonijiet

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

$$5\left(\sqrt{2}\right)^{2}-10\sqrt{3}\sqrt{2}+\sqrt{3}\sqrt{2}-2\left(\sqrt{3}\right)^{2}$$

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

$$5\times 2-10\sqrt{3}\sqrt{2}+\sqrt{3}\sqrt{2}-2\left(\sqrt{3}\right)^{2}$$

Immultiplika 5 u 2 biex tikseb 10.

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

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

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

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

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

Ikkombina -10\sqrt{6} u \sqrt{6} biex tikseb -9\sqrt{6}.

$$10-9\sqrt{6}-2\left(\sqrt{3}\right)^{2}$$

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

$$10-9\sqrt{6}-2\times 3$$

Immultiplika -2 u 3 biex tikseb -6.

$$10-9\sqrt{6}-6$$

Naqqas 6 minn 10 biex tikseb 4.

$$4-9\sqrt{6}$$