Issolvi (1-sqrt{18})(sqrt{2}+1/sqrt{2})

$$( 1 - \sqrt { 18 } ) ( \sqrt { 2 } + \frac { 1 } { \sqrt { 2 } } )$$

Evalwa

$$\frac{3\left(\sqrt{2}-6\right)}{2}\approx -6.878679656$$

Passi tas-Soluzzjonijiet

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\left(1-3\sqrt{2}\right)\left(\sqrt{2}+\frac{1}{\sqrt{2}}\right)$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\left(1-3\sqrt{2}\right)\left(\sqrt{2}+\frac{\sqrt{2}}{2}\right)$$

Ikkombina \sqrt{2} u \frac{\sqrt{2}}{2} biex tikseb \frac{3}{2}\sqrt{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 1-3\sqrt{2} b'\frac{3}{2}.

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

Esprimi -3\times \frac{3}{2} bħala frazzjoni waħda.

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

Immultiplika -3 u 3 biex tikseb -9.

$$\left(\frac{3}{2}+\frac{-9}{2}\sqrt{2}\right)\sqrt{2}$$

Frazzjoni \frac{-9}{2} tista' tinkiteb mill-ġdid bħala -\frac{9}{2} bl-estrazzjoni tas-sinjal negattiv.

$$\left(\frac{3}{2}-\frac{9}{2}\sqrt{2}\right)\sqrt{2}$$

Uża l-propjetà distributtiva biex timmultiplika \frac{3}{2}-\frac{9}{2}\sqrt{2} b'\sqrt{2}.

$$\frac{3}{2}\sqrt{2}-\frac{9}{2}\sqrt{2}\sqrt{2}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$\frac{3}{2}\sqrt{2}-\frac{9}{2}\times 2$$

Annulla 2 u 2.

$$\frac{3}{2}\sqrt{2}-9$$

Fattur

$$\frac{3 {(\sqrt{2} - 6)}}{2} = -6.878679656440358$$