Issolvi 51/56*sqrt{5/98}

$$\frac { 51 } { 56 } \times \sqrt { \frac { 5 } { 98 } }$$

Evalwa

$$\frac{51\sqrt{10}}{784}\approx 0.205709389$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{5}{98}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{5}}{\sqrt{98}}.

$$\frac{51}{56}\times \frac{\sqrt{5}}{\sqrt{98}}$$

Iffattura 98=7^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{7^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{7^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 7^{2}.

$$\frac{51}{56}\times \frac{\sqrt{5}}{7\sqrt{2}}$$

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

$$\frac{51}{56}\times \frac{\sqrt{5}\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{51}{56}\times \frac{\sqrt{5}\sqrt{2}}{7\times 2}$$

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

$$\frac{51}{56}\times \frac{\sqrt{10}}{7\times 2}$$

Immultiplika 7 u 2 biex tikseb 14.

$$\frac{51}{56}\times \frac{\sqrt{10}}{14}$$

Immultiplika \frac{51}{56} b'\frac{\sqrt{10}}{14} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{51\sqrt{10}}{56\times 14}$$

Immultiplika 56 u 14 biex tikseb 784.

$$\frac{51\sqrt{10}}{784}$$