Lahenda (4sqrt{2}-sqrt{3})(2sqrt{2}+5sqrt{3})=

$$( 4 \sqrt { 2 } - \sqrt { 3 } ) ( 2 \sqrt { 2 } + 5 \sqrt { 3 } ) =$$

Arvuta

$$18\sqrt{6}+1\approx 45,09081537$$

Lahenduse etapid

Rakendage distributiivsusomadus, korrutades avaldise 4\sqrt{2}-\sqrt{3} iga liikme avaldise 2\sqrt{2}+5\sqrt{3} iga liikmega.

$$8\left(\sqrt{2}\right)^{2}+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

\sqrt{2} ruut on 2.

$$8\times 2+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

Korrutage 8 ja 2, et leida 16.

$$16+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

\sqrt{3} ja \sqrt{2} korrutage numbrid, mis on sama juur.

$$16+20\sqrt{6}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

\sqrt{3} ja \sqrt{2} korrutage numbrid, mis on sama juur.

$$16+20\sqrt{6}-2\sqrt{6}-5\left(\sqrt{3}\right)^{2}$$

Kombineerige 20\sqrt{6} ja -2\sqrt{6}, et leida 18\sqrt{6}.

$$16+18\sqrt{6}-5\left(\sqrt{3}\right)^{2}$$

\sqrt{3} ruut on 3.

$$16+18\sqrt{6}-5\times 3$$

Korrutage -5 ja 3, et leida -15.

$$16+18\sqrt{6}-15$$

Lahutage 15 väärtusest 16, et leida 1.

$$1+18\sqrt{6}$$