Rešite =1/sqrt{2}*1/2div1/sqrt{2}*frac{sqrt{3}}{2}

$$= \frac { 1 } { \sqrt { 2 } } \cdot \frac { 1 } { 2 } \div \frac { 1 } { \sqrt { 2 } } \cdot \frac { \sqrt { 3 } } { 2 }$$

Ovrednoti

$$\frac{\sqrt{3}}{4}\approx 0,433012702$$

Koraki rešitve

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

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

Kvadrat vrednosti \sqrt{2} je 2.

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

Pomnožite \frac{\sqrt{2}}{2} s/z \frac{1}{2} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

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

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

Kvadrat vrednosti \sqrt{2} je 2.

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

Delite \frac{\sqrt{2}}{2\times 2} s/z \frac{\sqrt{2}}{2} tako, da pomnožite \frac{\sqrt{2}}{2\times 2} z obratno vrednostjo \frac{\sqrt{2}}{2}.

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

Okrajšaj 2\sqrt{2} v števcu in imenovalcu.

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

Pomnožite \frac{1}{2} s/z \frac{\sqrt{3}}{2} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Pomnožite 2 in 2, da dobite 4.

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