Lahenda (sqrt{10}-7sqrt{5})(3sqrt{10}+2sqrt{5})

$$( \sqrt { 10 } - 7 \sqrt { 5 } ) ( 3 \sqrt { 10 } + 2 \sqrt { 5 } )$$

Arvuta

$$-95\sqrt{2}-40\approx -174,350288425$$

Lahenduse etapid

Rakendage distributiivsusomadus, korrutades avaldise \sqrt{10}-7\sqrt{5} iga liikme avaldise 3\sqrt{10}+2\sqrt{5} iga liikmega.

$$3\left(\sqrt{10}\right)^{2}+2\sqrt{10}\sqrt{5}-21\sqrt{5}\sqrt{10}-14\left(\sqrt{5}\right)^{2}$$

\sqrt{10} ruut on 10.

$$3\times 10+2\sqrt{10}\sqrt{5}-21\sqrt{5}\sqrt{10}-14\left(\sqrt{5}\right)^{2}$$

Korrutage 3 ja 10, et leida 30.

$$30+2\sqrt{10}\sqrt{5}-21\sqrt{5}\sqrt{10}-14\left(\sqrt{5}\right)^{2}$$

Tegurda 10=5\times 2. Kirjutage \sqrt{5\times 2} toote juured, kui see ruut \sqrt{5}\sqrt{2}.

$$30+2\sqrt{5}\sqrt{2}\sqrt{5}-21\sqrt{5}\sqrt{10}-14\left(\sqrt{5}\right)^{2}$$

Korrutage \sqrt{5} ja \sqrt{5}, et leida 5.

$$30+2\times 5\sqrt{2}-21\sqrt{5}\sqrt{10}-14\left(\sqrt{5}\right)^{2}$$

Korrutage 2 ja 5, et leida 10.

$$30+10\sqrt{2}-21\sqrt{5}\sqrt{10}-14\left(\sqrt{5}\right)^{2}$$

Tegurda 10=5\times 2. Kirjutage \sqrt{5\times 2} toote juured, kui see ruut \sqrt{5}\sqrt{2}.

$$30+10\sqrt{2}-21\sqrt{5}\sqrt{5}\sqrt{2}-14\left(\sqrt{5}\right)^{2}$$

Korrutage \sqrt{5} ja \sqrt{5}, et leida 5.

$$30+10\sqrt{2}-21\times 5\sqrt{2}-14\left(\sqrt{5}\right)^{2}$$

Korrutage -21 ja 5, et leida -105.

$$30+10\sqrt{2}-105\sqrt{2}-14\left(\sqrt{5}\right)^{2}$$

Kombineerige 10\sqrt{2} ja -105\sqrt{2}, et leida -95\sqrt{2}.

$$30-95\sqrt{2}-14\left(\sqrt{5}\right)^{2}$$

\sqrt{5} ruut on 5.

$$30-95\sqrt{2}-14\times 5$$

Korrutage -14 ja 5, et leida -70.

$$30-95\sqrt{2}-70$$

Lahutage 70 väärtusest 30, et leida -40.

$$-40-95\sqrt{2}$$