Issolvi (1/2sqrt{3}-4sqrt{5})^2=

$$( \frac { 1 } { 2 } \sqrt { 3 } - 4 \sqrt { 5 } ) ^ { 2 } =$$

Evalwa

$$\frac{323}{4}-4\sqrt{15}\approx 65.258066615$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(\frac{1}{2}\sqrt{3}-4\sqrt{5}\right)^{2}.

$$\frac{1}{4}\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{1}{4}\times 3-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

Immultiplika \frac{1}{4} u 3 biex tikseb \frac{3}{4}.

$$\frac{3}{4}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\times 5$$

Immultiplika 16 u 5 biex tikseb 80.

$$\frac{3}{4}-4\sqrt{15}+80$$

Żid \frac{3}{4} u 80 biex tikseb \frac{323}{4}.

$$\frac{323}{4}-4\sqrt{15}$$

Espandi

$$\frac{323}{4} - 4 \sqrt{15} = 65.258066615$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(\frac{1}{2}\sqrt{3}-4\sqrt{5}\right)^{2}.

$$\frac{1}{4}\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{1}{4}\times 3-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

Immultiplika \frac{1}{4} u 3 biex tikseb \frac{3}{4}.

$$\frac{3}{4}-4\sqrt{3}\sqrt{5}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\left(\sqrt{5}\right)^{2}$$

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

$$\frac{3}{4}-4\sqrt{15}+16\times 5$$

Immultiplika 16 u 5 biex tikseb 80.

$$\frac{3}{4}-4\sqrt{15}+80$$

Żid \frac{3}{4} u 80 biex tikseb \frac{323}{4}.

$$\frac{323}{4}-4\sqrt{15}$$