Rešite (200sqrt{3}+50)*(50sqrt{2}+75sqrt{3})*(125sqrt{2}-18)div2

$$(200 \sqrt{ 3 } +50) \times (50 \sqrt{ 2 } +75 \sqrt{ 3 } ) \times (125 \sqrt{ 2 } -18) \div 2$$

Ovrednoti

$$144375\sqrt{6}+1216250\sqrt{3}+2790000\sqrt{2}-92500\approx 6313407,715340903$$

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost 200\sqrt{3}+50 z vsako vrednostjo 50\sqrt{2}+75\sqrt{3}.

$$\frac{\left(10000\sqrt{3}\sqrt{2}+15000\left(\sqrt{3}\right)^{2}+2500\sqrt{2}+3750\sqrt{3}\right)\left(125\sqrt{2}-18\right)}{2}$$

Če želite \sqrt{3} pomnožite in \sqrt{2}, pomnožite številke v kvadratni korenu.

$$\frac{\left(10000\sqrt{6}+15000\left(\sqrt{3}\right)^{2}+2500\sqrt{2}+3750\sqrt{3}\right)\left(125\sqrt{2}-18\right)}{2}$$

Kvadrat vrednosti \sqrt{3} je 3.

$$\frac{\left(10000\sqrt{6}+15000\times 3+2500\sqrt{2}+3750\sqrt{3}\right)\left(125\sqrt{2}-18\right)}{2}$$

Pomnožite 15000 in 3, da dobite 45000.

$$\frac{\left(10000\sqrt{6}+45000+2500\sqrt{2}+3750\sqrt{3}\right)\left(125\sqrt{2}-18\right)}{2}$$

Uporabite distributivnost tako, da pomnožite vsako vrednost 10000\sqrt{6}+45000+2500\sqrt{2}+3750\sqrt{3} z vsako vrednostjo 125\sqrt{2}-18.

$$\frac{1250000\sqrt{6}\sqrt{2}-180000\sqrt{6}+5625000\sqrt{2}-810000+312500\left(\sqrt{2}\right)^{2}-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Faktorizirajte 6=2\times 3. Znova napišite kvadratni koren izdelka \sqrt{2\times 3} kot produkt kvadratnih korenov \sqrt{2}\sqrt{3}.

$$\frac{1250000\sqrt{2}\sqrt{3}\sqrt{2}-180000\sqrt{6}+5625000\sqrt{2}-810000+312500\left(\sqrt{2}\right)^{2}-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Pomnožite \sqrt{2} in \sqrt{2}, da dobite 2.

$$\frac{1250000\times 2\sqrt{3}-180000\sqrt{6}+5625000\sqrt{2}-810000+312500\left(\sqrt{2}\right)^{2}-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Pomnožite 1250000 in 2, da dobite 2500000.

$$\frac{2500000\sqrt{3}-180000\sqrt{6}+5625000\sqrt{2}-810000+312500\left(\sqrt{2}\right)^{2}-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Kvadrat vrednosti \sqrt{2} je 2.

$$\frac{2500000\sqrt{3}-180000\sqrt{6}+5625000\sqrt{2}-810000+312500\times 2-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Pomnožite 312500 in 2, da dobite 625000.

$$\frac{2500000\sqrt{3}-180000\sqrt{6}+5625000\sqrt{2}-810000+625000-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Seštejte -810000 in 625000, da dobite -185000.

$$\frac{2500000\sqrt{3}-180000\sqrt{6}+5625000\sqrt{2}-185000-45000\sqrt{2}+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Združite 5625000\sqrt{2} in -45000\sqrt{2}, da dobite 5580000\sqrt{2}.

$$\frac{2500000\sqrt{3}-180000\sqrt{6}+5580000\sqrt{2}-185000+468750\sqrt{3}\sqrt{2}-67500\sqrt{3}}{2}$$

Če želite \sqrt{3} pomnožite in \sqrt{2}, pomnožite številke v kvadratni korenu.

$$\frac{2500000\sqrt{3}-180000\sqrt{6}+5580000\sqrt{2}-185000+468750\sqrt{6}-67500\sqrt{3}}{2}$$

Združite -180000\sqrt{6} in 468750\sqrt{6}, da dobite 288750\sqrt{6}.

$$\frac{2500000\sqrt{3}+288750\sqrt{6}+5580000\sqrt{2}-185000-67500\sqrt{3}}{2}$$

Združite 2500000\sqrt{3} in -67500\sqrt{3}, da dobite 2432500\sqrt{3}.

$$\frac{2432500\sqrt{3}+288750\sqrt{6}+5580000\sqrt{2}-185000}{2}$$

Faktoriziraj

$$625 {(231 \sqrt{6} + 1946 \sqrt{3} + 4464 \sqrt{2} - 148)} = 6313407,715340903$$