Issolvi 19*(sqrt{5}-sqrt{3}+sqrt{2})(sqrt{5}-sqrt{3}-sqrt{2})

$$19 \cdot ( \sqrt { 5 } - \sqrt { 3 } + \sqrt { 2 } ) ( \sqrt { 5 } - \sqrt { 3 } - \sqrt { 2 } )$$

Evalwa

$$114-38\sqrt{15}\approx -33.173367156$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika 19 b'\sqrt{5}-\sqrt{3}+\sqrt{2}.

$$\left(19\sqrt{5}-19\sqrt{3}+19\sqrt{2}\right)\left(\sqrt{5}-\sqrt{3}-\sqrt{2}\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 19\sqrt{5}-19\sqrt{3}+19\sqrt{2} b'kull terminu ta' \sqrt{5}-\sqrt{3}-\sqrt{2}.

$$19\left(\sqrt{5}\right)^{2}-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$19\times 5-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Immultiplika 19 u 5 biex tikseb 95.

$$95-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$95-19\sqrt{15}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Biex timmultiplika \sqrt{5} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{15}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Ikkombina -19\sqrt{15} u -19\sqrt{15} biex tikseb -38\sqrt{15}.

$$95-38\sqrt{15}-19\sqrt{10}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$95-38\sqrt{15}-19\sqrt{10}+19\times 3+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Immultiplika 19 u 3 biex tikseb 57.

$$95-38\sqrt{15}-19\sqrt{10}+57+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Żid 95 u 57 biex tikseb 152.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{10}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Ikkombina -19\sqrt{10} u 19\sqrt{10} biex tikseb 0.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{6}-19\left(\sqrt{2}\right)^{2}$$

Ikkombina 19\sqrt{6} u -19\sqrt{6} biex tikseb 0.

$$152-38\sqrt{15}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}-19\times 2$$

Immultiplika -19 u 2 biex tikseb -38.

$$152-38\sqrt{15}-38$$

Naqqas 38 minn 152 biex tikseb 114.

$$114-38\sqrt{15}$$