Lahenda sqrt{(6sqrt{6})^2+(6sqrt{2})^2}

$$\sqrt { ( 6 \sqrt { 6 } ) ^ { 2 } + ( 6 \sqrt { 2 } ) ^ { 2 } }$$

Arvuta

$$12\sqrt{2}\approx 16,970562748$$

Lahenduse etapid

Laiendage \left(6\sqrt{6}\right)^{2}.

$$\sqrt{6^{2}\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

Arvutage 2 aste 6 ja leidke 36.

$$\sqrt{36\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

\sqrt{6} ruut on 6.

$$\sqrt{36\times 6+\left(6\sqrt{2}\right)^{2}}$$

Korrutage 36 ja 6, et leida 216.

$$\sqrt{216+\left(6\sqrt{2}\right)^{2}}$$

Laiendage \left(6\sqrt{2}\right)^{2}.

$$\sqrt{216+6^{2}\left(\sqrt{2}\right)^{2}}$$

Arvutage 2 aste 6 ja leidke 36.

$$\sqrt{216+36\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} ruut on 2.

$$\sqrt{216+36\times 2}$$

Korrutage 36 ja 2, et leida 72.

$$\sqrt{216+72}$$

Liitke 216 ja 72, et leida 288.

$$\sqrt{288}$$

Tegurda 288=12^{2}\times 2. Kirjutage \sqrt{12^{2}\times 2} toote juured, kui see ruut \sqrt{12^{2}}\sqrt{2}. Leidke 12^{2} ruutjuur.

$$12\sqrt{2}$$