Issolvi (-2sqrt{5}-4sqrt{11})(5sqrt{5}-4sqrt{11})

$$( - 2 \sqrt { 5 } - 4 \sqrt { 11 } ) ( 5 \sqrt { 5 } - 4 \sqrt { 11 } )$$

Evalwa

$$126-12\sqrt{55}\approx 37.005618155$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' -2\sqrt{5}-4\sqrt{11} b'kull terminu ta' 5\sqrt{5}-4\sqrt{11}.

$$-10\left(\sqrt{5}\right)^{2}+8\sqrt{11}\sqrt{5}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

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

$$-10\times 5+8\sqrt{11}\sqrt{5}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

Immultiplika -10 u 5 biex tikseb -50.

$$-50+8\sqrt{11}\sqrt{5}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

Biex timmultiplika \sqrt{11} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$-50+8\sqrt{55}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

Biex timmultiplika \sqrt{11} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$-50+8\sqrt{55}-20\sqrt{55}+16\left(\sqrt{11}\right)^{2}$$

Ikkombina 8\sqrt{55} u -20\sqrt{55} biex tikseb -12\sqrt{55}.

$$-50-12\sqrt{55}+16\left(\sqrt{11}\right)^{2}$$

Il-kwadrat ta' \sqrt{11} huwa 11.

$$-50-12\sqrt{55}+16\times 11$$

Immultiplika 16 u 11 biex tikseb 176.

$$-50-12\sqrt{55}+176$$

Żid -50 u 176 biex tikseb 126.

$$126-12\sqrt{55}$$

Fattur

$$6 {(21 - 2 \sqrt{55})} = 37.005618155$$