Issolvi (sqrt{3}+sqrt{10})(sqrt{3}-2sqrt{10})

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

Evalwa

$$-\sqrt{30}-17\approx -22.477225575$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' \sqrt{3}+\sqrt{10} b'kull terminu ta' \sqrt{3}-2\sqrt{10}.

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

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

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

Biex timmultiplika \sqrt{3} u \sqrt{10}, immultiplika n-numri taħt l-għerq kwadrat.

$$3-2\sqrt{30}+\sqrt{10}\sqrt{3}-2\left(\sqrt{10}\right)^{2}$$

Biex timmultiplika \sqrt{10} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$3-2\sqrt{30}+\sqrt{30}-2\left(\sqrt{10}\right)^{2}$$

Ikkombina -2\sqrt{30} u \sqrt{30} biex tikseb -\sqrt{30}.

$$3-\sqrt{30}-2\left(\sqrt{10}\right)^{2}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$3-\sqrt{30}-2\times 10$$

Immultiplika -2 u 10 biex tikseb -20.

$$3-\sqrt{30}-20$$

Naqqas 20 minn 3 biex tikseb -17.

$$-17-\sqrt{30}$$