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

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

Evalwa

$$-\sqrt{15}-1\approx -4.872983346$$

Passi tas-Soluzzjonijiet

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

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

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

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

Biex timmultiplika \sqrt{5} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$5+\sqrt{15}-2\sqrt{3}\sqrt{5}-2\left(\sqrt{3}\right)^{2}$$

Biex timmultiplika \sqrt{3} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$5+\sqrt{15}-2\sqrt{15}-2\left(\sqrt{3}\right)^{2}$$

Ikkombina \sqrt{15} u -2\sqrt{15} biex tikseb -\sqrt{15}.

$$5-\sqrt{15}-2\left(\sqrt{3}\right)^{2}$$

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

$$5-\sqrt{15}-2\times 3$$

Immultiplika -2 u 3 biex tikseb -6.

$$5-\sqrt{15}-6$$

Naqqas 6 minn 5 biex tikseb -1.

$$-1-\sqrt{15}$$