Lahenda frac{sqrt{3}+sqrt{6}+sqrt{2}+1+2sqrt{8}}{2}

$$\frac{ \sqrt{ 3 } + \sqrt{ 6 } + \sqrt{ 2 } +1+2 \sqrt{ 8 } }{ 2 }$$

Arvuta

$$\frac{\sqrt{3}+\sqrt{6}+5\sqrt{2}+1}{2}\approx 6,126304181$$

Lahenduse etapid

Tegurda 8=2^{2}\times 2. Kirjutage \sqrt{2^{2}\times 2} toote juured, kui see ruut \sqrt{2^{2}}\sqrt{2}. Leidke 2^{2} ruutjuur.

$$\frac{\sqrt{3}+\sqrt{6}+\sqrt{2}+1+2\times 2\sqrt{2}}{2}$$

Korrutage 2 ja 2, et leida 4.

$$\frac{\sqrt{3}+\sqrt{6}+\sqrt{2}+1+4\sqrt{2}}{2}$$

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

$$\frac{\sqrt{3}+\sqrt{6}+5\sqrt{2}+1}{2}$$