Issolvi frac{5sqrt{7}*sqrt{3}}{sqrt{28}}

$$\frac { 5 \sqrt { 7 } \times \sqrt { 3 } } { \sqrt { 28 } }$$

Evalwa

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Passi tas-Soluzzjonijiet

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

$$\frac{5\sqrt{21}}{\sqrt{28}}$$

Iffattura 28=2^{2}\times 7. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 7} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{7}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{5\sqrt{21}}{2\sqrt{7}}$$

Irrazzjonalizza d-denominatur tal-\frac{5\sqrt{21}}{2\sqrt{7}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{7}.

$$\frac{5\sqrt{21}\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

Il-kwadrat ta' \sqrt{7} huwa 7.

$$\frac{5\sqrt{21}\sqrt{7}}{2\times 7}$$

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}.

$$\frac{5\sqrt{7}\sqrt{3}\sqrt{7}}{2\times 7}$$

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

$$\frac{5\times 7\sqrt{3}}{2\times 7}$$

Immultiplika 2 u 7 biex tikseb 14.

$$\frac{5\times 7\sqrt{3}}{14}$$

Immultiplika 5 u 7 biex tikseb 35.

$$\frac{35\sqrt{3}}{14}$$

Iddividi 35\sqrt{3} b'14 biex tikseb\frac{5}{2}\sqrt{3}.

$$\frac{5}{2}\sqrt{3}$$