Lahenda (sqrt{8}-2sqrt{025)}-(sqrt{11/8}+sqrt{50}+2/3sqrt{12})

$$( \sqrt { 8 } - 2 \sqrt { 025 ) } - ( \sqrt { 1 \frac { 1 } { 8 } } + \sqrt { 50 } + \frac { 2 } { 3 } \sqrt { 12 } )$$

Arvuta

$$-\frac{4\sqrt{3}}{3}-\frac{15\sqrt{2}}{4}-10\approx -17,612701936$$

Lahenduse etapid

Tegurda 8=2^{2}\times 2. Kirjutage korrutise ruutjuur \sqrt{2^{2}\times 2} ümber ruutjuurte korrutisena \sqrt{2^{2}}\sqrt{2}. Leidke 2^{2} ruutjuur.

$$2\sqrt{2}-2\sqrt{25}-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Arvutage 25 ruutjuur, et saada 5.

$$2\sqrt{2}-2\times 5-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Korrutage -2 ja 5, et leida -10.

$$2\sqrt{2}-10-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Korrutage 1 ja 8, et leida 8.

$$2\sqrt{2}-10-\left(\sqrt{\frac{8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Liitke 8 ja 1, et leida 9.

$$2\sqrt{2}-10-\left(\sqrt{\frac{9}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Kirjutage jagamise ruutjuur \sqrt{\frac{9}{8}} ümber ruutjuurte jagamisena \frac{\sqrt{9}}{\sqrt{8}}.

$$2\sqrt{2}-10-\left(\frac{\sqrt{9}}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Arvutage 9 ruutjuur, et saada 3.

$$2\sqrt{2}-10-\left(\frac{3}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tegurda 8=2^{2}\times 2. Kirjutage korrutise ruutjuur \sqrt{2^{2}\times 2} ümber ruutjuurte korrutisena \sqrt{2^{2}}\sqrt{2}. Leidke 2^{2} ruutjuur.

$$2\sqrt{2}-10-\left(\frac{3}{2\sqrt{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Vabastage \frac{3}{2\sqrt{2}} nimetaja irratsionaalsusest, korrutades lugeja ja nimetaja arvuga \sqrt{2}.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

\sqrt{2} ruut on 2.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\times 2}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Korrutage 2 ja 2, et leida 4.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tegurda 50=5^{2}\times 2. Kirjutage korrutise ruutjuur \sqrt{5^{2}\times 2} ümber ruutjuurte korrutisena \sqrt{5^{2}}\sqrt{2}. Leidke 5^{2} ruutjuur.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+5\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Kombineerige \frac{3\sqrt{2}}{4} ja 5\sqrt{2}, et leida \frac{23}{4}\sqrt{2}.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Tegurda 12=2^{2}\times 3. Kirjutage korrutise ruutjuur \sqrt{2^{2}\times 3} ümber ruutjuurte korrutisena \sqrt{2^{2}}\sqrt{3}. Leidke 2^{2} ruutjuur.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\times 2\sqrt{3}\right)$$

Avaldage \frac{2}{3}\times 2 ühe murdarvuna.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2\times 2}{3}\sqrt{3}\right)$$

Korrutage 2 ja 2, et leida 4.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}\right)$$

Avaldise "\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}" vastandi leidmiseks tuleb leida iga liikme vastand.

$$2\sqrt{2}-10-\frac{23}{4}\sqrt{2}-\frac{4}{3}\sqrt{3}$$

Kombineerige 2\sqrt{2} ja -\frac{23}{4}\sqrt{2}, et leida -\frac{15}{4}\sqrt{2}.

$$-\frac{15}{4}\sqrt{2}-10-\frac{4}{3}\sqrt{3}$$

Lahuta teguriteks

$$\frac{-16 \sqrt{3} - 45 \sqrt{2} - 120}{12} = -17,612701935657608$$