Resol 1/sqrt{2}=(frac{sqrt{2}}{sqrt{2}*sqrt{2}})=frac{sqrt{2}}{2}

$$\frac { 1 } { \sqrt { 2 } } = ( \frac { \sqrt { 2 } } { \sqrt { 2 } \cdot \sqrt { 2 } } ) = \frac { \sqrt { 2 } } { 2 }$$

Verifiqueu

Passos de solució

Multipliqueu \sqrt{2} per \sqrt{2} per obtenir 2.

$$\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\text{ and }\frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}=\frac{\sqrt{2}}{2}$$

Multipliqueu \sqrt{2} per \sqrt{2} per obtenir 2.

$$\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\text{ and }\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

Racionalitzeu el denominador de \frac{1}{\sqrt{2}} multiplicant el numerador i el denominador per \sqrt{2}.

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{\sqrt{2}}{2}\text{ and }\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

L'arrel quadrada de \sqrt{2} és 2.

$$\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\text{ and }\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

Resteu \frac{\sqrt{2}}{2} en tots dos costats.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}=0\text{ and }\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

Combineu \frac{\sqrt{2}}{2} i -\frac{\sqrt{2}}{2} per obtenir 0.

$$0=0\text{ and }\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

Compareu 0 amb 0.

$$\text{true}\text{ and }\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

Resteu \frac{\sqrt{2}}{2} en tots dos costats.

$$\text{true}\text{ and }\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}=0$$

Combineu \frac{\sqrt{2}}{2} i -\frac{\sqrt{2}}{2} per obtenir 0.

$$\text{true}\text{ and }0=0$$

Compareu 0 amb 0.

$$\text{true}\text{ and }\text{true}$$

La conjunció de \text{true} i \text{true} és \text{true}.

$$\text{true}$$