Issolvi {left(3sqrt{2}-2sqrt{3}right)}^2

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

Evalwa

$$30-12\sqrt{6}\approx 0.606123087$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3\sqrt{2}-2\sqrt{3}\right)^{2}.

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

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

$$9\times 2-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Immultiplika 9 u 2 biex tikseb 18.

$$18-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

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

$$18-12\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

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

$$18-12\sqrt{6}+4\times 3$$

Immultiplika 4 u 3 biex tikseb 12.

$$18-12\sqrt{6}+12$$

Żid 18 u 12 biex tikseb 30.

$$30-12\sqrt{6}$$

Espandi

$$30-12\sqrt{6}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3\sqrt{2}-2\sqrt{3}\right)^{2}.

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

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

$$9\times 2-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Immultiplika 9 u 2 biex tikseb 18.

$$18-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

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

$$18-12\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

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

$$18-12\sqrt{6}+4\times 3$$

Immultiplika 4 u 3 biex tikseb 12.

$$18-12\sqrt{6}+12$$

Żid 18 u 12 biex tikseb 30.

$$30-12\sqrt{6}$$