Issolvi frac{sqrt{18}}{8}sqrt{27/2}

$$\frac{ \sqrt{ 18 } }{ 8 } \sqrt{ \frac{ 27 }{ 2 } }$$

Evalwa

$$\frac{9\sqrt{3}}{8}\approx 1.948557159$$

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}.

$$\frac{3\sqrt{2}}{8}\sqrt{\frac{27}{2}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{27}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{27}}{\sqrt{2}}.

$$\frac{3\sqrt{2}}{8}\times \frac{\sqrt{27}}{\sqrt{2}}$$

Iffattura 27=3^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{3\sqrt{2}}{8}\times \frac{3\sqrt{3}}{\sqrt{2}}$$

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

$$\frac{3\sqrt{2}}{8}\times \frac{3\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{3\sqrt{2}}{8}\times \frac{3\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{3\sqrt{2}}{8}\times \frac{3\sqrt{6}}{2}$$

Immultiplika \frac{3\sqrt{2}}{8} b'\frac{3\sqrt{6}}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{3\sqrt{2}\times 3\sqrt{6}}{8\times 2}$$

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

$$\frac{3\sqrt{2}\times 3\sqrt{2}\sqrt{3}}{8\times 2}$$

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

$$\frac{3\times 2\times 3\sqrt{3}}{8\times 2}$$

Immultiplika 3 u 2 biex tikseb 6.

$$\frac{6\times 3\sqrt{3}}{8\times 2}$$

Immultiplika 6 u 3 biex tikseb 18.

$$\frac{18\sqrt{3}}{8\times 2}$$

Immultiplika 8 u 2 biex tikseb 16.

$$\frac{18\sqrt{3}}{16}$$

Iddividi 18\sqrt{3} b'16 biex tikseb\frac{9}{8}\sqrt{3}.

$$\frac{9}{8}\sqrt{3}$$