Issolvi (4sqrt{6}-4sqrt{1/2}+3sqrt{8})div2sqrt{2}=

$$( 4 \sqrt { 6 } - 4 \sqrt { \frac { 1 } { 2 } } + 3 \sqrt { 8 } ) \div 2 \sqrt { 2 } =$$

Evalwa

$$4\left(\sqrt{3}+1\right)\approx 10.92820323$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{1}}{\sqrt{2}}+3\sqrt{8}}{2}\sqrt{2}$$

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

$$\frac{4\sqrt{6}-4\times \frac{1}{\sqrt{2}}+3\sqrt{8}}{2}\sqrt{2}$$

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

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+3\sqrt{8}}{2}\sqrt{2}$$

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

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{2}}{2}+3\sqrt{8}}{2}\sqrt{2}$$

Ikkanċella l-akbar fattur komuni 2 f'4 u 2.

$$\frac{4\sqrt{6}-2\sqrt{2}+3\sqrt{8}}{2}\sqrt{2}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{4\sqrt{6}-2\sqrt{2}+3\times 2\sqrt{2}}{2}\sqrt{2}$$

Immultiplika 3 u 2 biex tikseb 6.

$$\frac{4\sqrt{6}-2\sqrt{2}+6\sqrt{2}}{2}\sqrt{2}$$

Ikkombina -2\sqrt{2} u 6\sqrt{2} biex tikseb 4\sqrt{2}.

$$\frac{4\sqrt{6}+4\sqrt{2}}{2}\sqrt{2}$$

Esprimi \frac{4\sqrt{6}+4\sqrt{2}}{2}\sqrt{2} bħala frazzjoni waħda.

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

Uża l-propjetà distributtiva biex timmultiplika 4\sqrt{6}+4\sqrt{2} b'\sqrt{2}.

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

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}.

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

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

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

Immultiplika 4 u 2 biex tikseb 8.

$$\frac{8\sqrt{3}+4\left(\sqrt{2}\right)^{2}}{2}$$

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

$$\frac{8\sqrt{3}+4\times 2}{2}$$

Immultiplika 4 u 2 biex tikseb 8.

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