Issolvi (4sqrt{2}-3sqrt{6})(2sqrt{6}+3sqrt{2})

$$( 4 \sqrt { 2 } - 3 \sqrt { 6 } ) ( 2 \sqrt { 6 } + 3 \sqrt { 2 } )$$

Evalwa

$$-2\sqrt{3}-12\approx -15.464101615$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 4\sqrt{2}-3\sqrt{6} b'kull terminu ta' 2\sqrt{6}+3\sqrt{2}.

$$8\sqrt{2}\sqrt{6}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

$$8\sqrt{2}\sqrt{2}\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$8\times 2\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Immultiplika 8 u 2 biex tikseb 16.

$$16\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

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

$$16\sqrt{3}+12\times 2-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Immultiplika 12 u 2 biex tikseb 24.

$$16\sqrt{3}+24-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$16\sqrt{3}+24-6\times 6-9\sqrt{6}\sqrt{2}$$

Immultiplika -6 u 6 biex tikseb -36.

$$16\sqrt{3}+24-36-9\sqrt{6}\sqrt{2}$$

Naqqas 36 minn 24 biex tikseb -12.

$$16\sqrt{3}-12-9\sqrt{6}\sqrt{2}$$

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

$$16\sqrt{3}-12-9\sqrt{2}\sqrt{3}\sqrt{2}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$16\sqrt{3}-12-9\times 2\sqrt{3}$$

Immultiplika -9 u 2 biex tikseb -18.

$$16\sqrt{3}-12-18\sqrt{3}$$

Ikkombina 16\sqrt{3} u -18\sqrt{3} biex tikseb -2\sqrt{3}.

$$-2\sqrt{3}-12$$

Fattur

$$2 {(-\sqrt{3} - 6)} = -15.464101615$$