Issolvi 12sqrt{1/6}div3sqrt{7/12}*1/2sqrt{101/2}

$$12 \sqrt { \frac { 1 } { 6 } } \div 3 \sqrt { \frac { 7 } { 12 } } \times \frac { 1 } { 2 } \sqrt { 10 \frac { 1 } { 2 } }$$

Evalwa

$$\frac{7\sqrt{3}}{6}\approx 2.020725942$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{6}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{6}}.

$$\frac{12\times \frac{\sqrt{1}}{\sqrt{6}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

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

$$\frac{12\times \frac{1}{\sqrt{6}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

$$\frac{12\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{12\times \frac{\sqrt{6}}{6}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Ikkanċella l-akbar fattur komuni 6 f'12 u 6.

$$\frac{2\sqrt{6}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{7}{12}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{7}}{\sqrt{12}}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}}{\sqrt{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}}{2\sqrt{3}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{7}}{2\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}\sqrt{3}}{2\times 3}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Biex timmultiplika \sqrt{7} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{2\times 3}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Immultiplika 10 u 2 biex tikseb 20.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{20+1}{2}}$$

Żid 20 u 1 biex tikseb 21.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{21}{2}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{21}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{21}}{\sqrt{2}}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}}{\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{21}}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}\sqrt{2}}{2}$$

Biex timmultiplika \sqrt{21} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Immultiplika \frac{2\sqrt{6}}{3} b'\frac{\sqrt{21}}{6} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{2\sqrt{6}\sqrt{21}}{3\times 6}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{\sqrt{6}\sqrt{21}}{3\times 3}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Immultiplika \frac{\sqrt{6}\sqrt{21}}{3\times 3} b'\frac{1}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\sqrt{6}\sqrt{21}}{3\times 3\times 2}\times \frac{\sqrt{42}}{2}$$

Immultiplika \frac{\sqrt{6}\sqrt{21}}{3\times 3\times 2} b'\frac{\sqrt{42}}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\sqrt{6}\sqrt{21}\sqrt{42}}{3\times 3\times 2\times 2}$$

Iffattura 42=6\times 7. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{6\times 7} bħala l-prodott tal-għeruq kwadrati \sqrt{6}\sqrt{7}.

$$\frac{\sqrt{6}\sqrt{21}\sqrt{6}\sqrt{7}}{3\times 3\times 2\times 2}$$

Immultiplika \sqrt{6} u \sqrt{6} biex tikseb 6.

$$\frac{6\sqrt{21}\sqrt{7}}{3\times 3\times 2\times 2}$$

Iffattura 21=7\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{7\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{7}\sqrt{3}.

$$\frac{6\sqrt{7}\sqrt{3}\sqrt{7}}{3\times 3\times 2\times 2}$$

Immultiplika \sqrt{7} u \sqrt{7} biex tikseb 7.

$$\frac{6\times 7\sqrt{3}}{3\times 3\times 2\times 2}$$

Immultiplika 6 u 7 biex tikseb 42.

$$\frac{42\sqrt{3}}{3\times 3\times 2\times 2}$$

Immultiplika 3 u 3 biex tikseb 9.

$$\frac{42\sqrt{3}}{9\times 2\times 2}$$

Immultiplika 9 u 2 biex tikseb 18.

$$\frac{42\sqrt{3}}{18\times 2}$$

Immultiplika 18 u 2 biex tikseb 36.

$$\frac{42\sqrt{3}}{36}$$

Iddividi 42\sqrt{3} b'36 biex tikseb\frac{7}{6}\sqrt{3}.

$$\frac{7}{6}\sqrt{3}$$