Issolvi frac{4sqrt{3}}{sqrt{2}}+sqrt{2}(sqrt{3}-3sqrt{2})

$$\frac { 4 \sqrt { 3 } } { \sqrt { 2 } } + \sqrt { 2 } ( \sqrt { 3 } - 3 \sqrt { 2 } )$$

Evalwa

$$3\left(\sqrt{6}-2\right)\approx 1.348469228$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{4\sqrt{3}}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{2}\left(\sqrt{3}-3\sqrt{2}\right)$$

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

$$\frac{4\sqrt{3}\sqrt{2}}{2}+\sqrt{2}\left(\sqrt{3}-3\sqrt{2}\right)$$

Biex timmultiplika \sqrt{3} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{4\sqrt{6}}{2}+\sqrt{2}\left(\sqrt{3}-3\sqrt{2}\right)$$

Iddividi 4\sqrt{6} b'2 biex tikseb2\sqrt{6}.

$$2\sqrt{6}+\sqrt{2}\left(\sqrt{3}-3\sqrt{2}\right)$$

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

$$2\sqrt{6}+\sqrt{2}\sqrt{3}-3\left(\sqrt{2}\right)^{2}$$

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$2\sqrt{6}+\sqrt{6}-3\left(\sqrt{2}\right)^{2}$$

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

$$2\sqrt{6}+\sqrt{6}-3\times 2$$

Immultiplika -3 u 2 biex tikseb -6.

$$2\sqrt{6}+\sqrt{6}-6$$

Ikkombina 2\sqrt{6} u \sqrt{6} biex tikseb 3\sqrt{6}.

$$3\sqrt{6}-6$$

Fattur

$$3 {(\sqrt{6} - 2)} = 1.348469228$$