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

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

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Lahenduse etapid

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{2} nimetaja \frac{1}{\sqrt{2}} nimetaja.

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

\sqrt{2} ruut on 2.

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

Lahutage mõlemast poolest \frac{\sqrt{2}}{2}.

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

Kombineerige \frac{\sqrt{2}}{2} ja -\frac{\sqrt{2}}{2}, et leida 0.

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

Võrrelge omavahel 0 ja 0.

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

Lahutage mõlemast poolest \frac{\sqrt{2}}{2}.

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

Kombineerige \frac{\sqrt{2}}{2} ja -\frac{\sqrt{2}}{2}, et leida 0.

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

Võrrelge omavahel 0 ja 0.

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

\text{true} ja \text{true} konjunktsioon on \text{true}.

$$\text{true}$$