Issolvi (10sqrt{6}+10sqrt{2})^2

$$( 10 \sqrt { 6 } + 10 \sqrt { 2 } ) ^ { 2 }$$

Evalwa

$$400\left(\sqrt{3}+2\right)\approx 1492.820323028$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(10\sqrt{6}+10\sqrt{2}\right)^{2}.

$$100\left(\sqrt{6}\right)^{2}+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$100\times 6+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Immultiplika 100 u 6 biex tikseb 600.

$$600+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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}.

$$600+200\sqrt{2}\sqrt{3}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\times 2\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Immultiplika 200 u 2 biex tikseb 400.

$$600+400\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+400\sqrt{3}+100\times 2$$

Immultiplika 100 u 2 biex tikseb 200.

$$600+400\sqrt{3}+200$$

Żid 600 u 200 biex tikseb 800.

$$800+400\sqrt{3}$$

Espandi

$$400 \sqrt{3} + 800 = 1492.820323028$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(10\sqrt{6}+10\sqrt{2}\right)^{2}.

$$100\left(\sqrt{6}\right)^{2}+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$100\times 6+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Immultiplika 100 u 6 biex tikseb 600.

$$600+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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}.

$$600+200\sqrt{2}\sqrt{3}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\times 2\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Immultiplika 200 u 2 biex tikseb 400.

$$600+400\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+400\sqrt{3}+100\times 2$$

Immultiplika 100 u 2 biex tikseb 200.

$$600+400\sqrt{3}+200$$

Żid 600 u 200 biex tikseb 800.

$$800+400\sqrt{3}$$