Rešite 1/sqrt{2}frac{sqrt{2}}{3}1/2sqrt{2}

$$\frac { 1 } { \sqrt { 2 } } \frac { \sqrt { 2 } } { 3 } \frac { 1 } { 2 \sqrt { 2 } }$$

Ovrednoti

$$\frac{\sqrt{2}}{12}\approx 0,11785113$$

Koraki rešitve

Racionalizirajte imenovalec \frac{1}{\sqrt{2}} tako, da pomnožite števec in imenovalec s \sqrt{2}.

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{2}}{3}\times \frac{1}{2\sqrt{2}}$$

Kvadrat vrednosti \sqrt{2} je 2.

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

Racionalizirajte imenovalec \frac{1}{2\sqrt{2}} tako, da pomnožite števec in imenovalec s \sqrt{2}.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{3}\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

Kvadrat vrednosti \sqrt{2} je 2.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{3}\times \frac{\sqrt{2}}{2\times 2}$$

Pomnožite 2 in 2, da dobite 4.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{3}\times \frac{\sqrt{2}}{4}$$

Pomnožite \frac{\sqrt{2}}{2} s/z \frac{\sqrt{2}}{3} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\sqrt{2}\sqrt{2}}{2\times 3}\times \frac{\sqrt{2}}{4}$$

Pomnožite \frac{\sqrt{2}\sqrt{2}}{2\times 3} s/z \frac{\sqrt{2}}{4} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{2}}{2\times 3\times 4}$$

Pomnožite \sqrt{2} in \sqrt{2}, da dobite 2.

$$\frac{2\sqrt{2}}{2\times 3\times 4}$$

Okrajšaj 2 v števcu in imenovalcu.

$$\frac{\sqrt{2}}{3\times 4}$$

Pomnožite 3 in 4, da dobite 12.

$$\frac{\sqrt{2}}{12}$$