Issolvi sqrt{30}*3/2sqrt{22/3}+(-2sqrt{21/2})

$$\sqrt { 30 } \times \frac { 3 } { 2 } \sqrt { 2 \frac { 2 } { 3 } } + ( - 2 \sqrt { 2 \frac { 1 } { 2 } } )$$

Evalwa

$$6\sqrt{5}-\sqrt{10}\approx 10.254130205$$

Passi tas-Soluzzjonijiet

Immultiplika 2 u 3 biex tikseb 6.

$$\sqrt{30}\times \frac{3}{2}\sqrt{\frac{6+2}{3}}-2\sqrt{\frac{2\times 2+1}{2}}$$

Żid 6 u 2 biex tikseb 8.

$$\sqrt{30}\times \frac{3}{2}\sqrt{\frac{8}{3}}-2\sqrt{\frac{2\times 2+1}{2}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{8}{3}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{8}}{\sqrt{3}}.

$$\sqrt{30}\times \frac{3}{2}\times \frac{\sqrt{8}}{\sqrt{3}}-2\sqrt{\frac{2\times 2+1}{2}}$$

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}.

$$\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{2}}{\sqrt{3}}-2\sqrt{\frac{2\times 2+1}{2}}$$

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

$$\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-2\sqrt{\frac{2\times 2+1}{2}}$$

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

$$\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{2}\sqrt{3}}{3}-2\sqrt{\frac{2\times 2+1}{2}}$$

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

$$\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{6}}{3}-2\sqrt{\frac{2\times 2+1}{2}}$$

Esprimi \sqrt{30}\times \frac{2\sqrt{6}}{3} bħala frazzjoni waħda.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\sqrt{\frac{2\times 2+1}{2}}$$

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\sqrt{\frac{4+1}{2}}$$

Żid 4 u 1 biex tikseb 5.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\sqrt{\frac{5}{2}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{5}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\times \frac{\sqrt{5}}{\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{5}}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\times \frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\times \frac{\sqrt{5}\sqrt{2}}{2}$$

Biex timmultiplika \sqrt{5} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-2\times \frac{\sqrt{10}}{2}$$

Annulla 2 u 2.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}-\sqrt{10}$$

Iffattura 30=6\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{6\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{6}\sqrt{5}.

$$\frac{\sqrt{6}\sqrt{5}\times 2\sqrt{6}}{3}\times \frac{3}{2}-\sqrt{10}$$

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

$$\frac{6\times 2\sqrt{5}}{3}\times \frac{3}{2}-\sqrt{10}$$

Immultiplika 6 u 2 biex tikseb 12.

$$\frac{12\sqrt{5}}{3}\times \frac{3}{2}-\sqrt{10}$$

Iddividi 12\sqrt{5} b'3 biex tikseb4\sqrt{5}.

$$4\sqrt{5}\times \frac{3}{2}-\sqrt{10}$$

Esprimi 4\times \frac{3}{2} bħala frazzjoni waħda.

$$\frac{4\times 3}{2}\sqrt{5}-\sqrt{10}$$

Immultiplika 4 u 3 biex tikseb 12.

$$\frac{12}{2}\sqrt{5}-\sqrt{10}$$

Iddividi 12 b'2 biex tikseb6.

$$6\sqrt{5}-\sqrt{10}$$

Fattur

$$6 \sqrt{5} - \sqrt{10} = 10.254130205$$