Lahenda (4sqrt{2}-3sqrt{6})(2sqrt{6}+3sqrt{2})

$$( 4 \sqrt { 2 } - 3 \sqrt { 6 } ) ( 2 \sqrt { 6 } + 3 \sqrt { 2 } )$$

Arvuta

$$-2\sqrt{3}-12\approx -15,464101615$$

Lahenduse etapid

Rakendage distributiivsusomadus, korrutades avaldise 4\sqrt{2}-3\sqrt{6} iga liikme avaldise 2\sqrt{6}+3\sqrt{2} iga liikmega.

$$8\sqrt{2}\sqrt{6}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

$$8\sqrt{2}\sqrt{2}\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

$$8\times 2\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Korrutage 8 ja 2, et leida 16.

$$16\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

\sqrt{2} ruut on 2.

$$16\sqrt{3}+12\times 2-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Korrutage 12 ja 2, et leida 24.

$$16\sqrt{3}+24-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

\sqrt{6} ruut on 6.

$$16\sqrt{3}+24-6\times 6-9\sqrt{6}\sqrt{2}$$

Korrutage -6 ja 6, et leida -36.

$$16\sqrt{3}+24-36-9\sqrt{6}\sqrt{2}$$

Lahutage 36 väärtusest 24, et leida -12.

$$16\sqrt{3}-12-9\sqrt{6}\sqrt{2}$$

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

$$16\sqrt{3}-12-9\sqrt{2}\sqrt{3}\sqrt{2}$$

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

$$16\sqrt{3}-12-9\times 2\sqrt{3}$$

Korrutage -9 ja 2, et leida -18.

$$16\sqrt{3}-12-18\sqrt{3}$$

Kombineerige 16\sqrt{3} ja -18\sqrt{3}, et leida -2\sqrt{3}.

$$-2\sqrt{3}-12$$

Lahuta teguriteks

$$2 {(-\sqrt{3} - 6)} = -15,464101615$$