Issolvi (sqrt{15}+sqrt{3})^2

$$( \sqrt { 15 } + \sqrt { 3 } ) ^ { 2 }$$

Evalwa

$$6\left(\sqrt{5}+3\right)\approx 31.416407865$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{15}+\sqrt{3}\right)^{2}.

$$\left(\sqrt{15}\right)^{2}+2\sqrt{15}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

Il-kwadrat ta' \sqrt{15} huwa 15.

$$15+2\sqrt{15}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

Iffattura 15=3\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{5}.

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

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$15+2\times 3\sqrt{5}+\left(\sqrt{3}\right)^{2}$$

Immultiplika 2 u 3 biex tikseb 6.

$$15+6\sqrt{5}+\left(\sqrt{3}\right)^{2}$$

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

$$15+6\sqrt{5}+3$$

Żid 15 u 3 biex tikseb 18.

$$18+6\sqrt{5}$$

Espandi

$$6 \sqrt{5} + 18 = 31.416407865$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{15}+\sqrt{3}\right)^{2}.

$$\left(\sqrt{15}\right)^{2}+2\sqrt{15}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

Il-kwadrat ta' \sqrt{15} huwa 15.

$$15+2\sqrt{15}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

Iffattura 15=3\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{5}.

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

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$15+2\times 3\sqrt{5}+\left(\sqrt{3}\right)^{2}$$

Immultiplika 2 u 3 biex tikseb 6.

$$15+6\sqrt{5}+\left(\sqrt{3}\right)^{2}$$

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

$$15+6\sqrt{5}+3$$

Żid 15 u 3 biex tikseb 18.

$$18+6\sqrt{5}$$