Issolvi frac{sqrt{59}*29-sqrt{5*29}}{sqrt{59*29}+sqrt{5*29}}

$$\frac { \sqrt { 59 } \cdot 29 - \sqrt { 5 \cdot 29 } } { \sqrt { 59 \cdot 29 } + \sqrt { 5 \cdot 29 } }$$

Evalwa

$$\frac{59\sqrt{29}+5-\sqrt{295}-\sqrt{8555}}{54}\approx 3.945479937$$

Passi tas-Soluzzjonijiet

Immultiplika 5 u 29 biex tikseb 145.

$$\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{59\times 29}+\sqrt{5\times 29}}$$

Immultiplika 59 u 29 biex tikseb 1711.

$$\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{5\times 29}}$$

Immultiplika 5 u 29 biex tikseb 145.

$$\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{145}}$$

Irrazzjonalizza d-denominatur tal-\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{145}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{1711}-\sqrt{145}.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{\left(\sqrt{1711}+\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}$$

Ikkunsidra li \left(\sqrt{1711}+\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{\left(\sqrt{1711}\right)^{2}-\left(\sqrt{145}\right)^{2}}$$

Ikkwadra \sqrt{1711}. Ikkwadra \sqrt{145}.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{1711-145}$$

Naqqas 145 minn 1711 biex tikseb 1566.

$$\frac{\left(29\sqrt{59}-\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right)}{1566}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 29\sqrt{59}-\sqrt{145} b'kull terminu ta' \sqrt{1711}-\sqrt{145}.

$$\frac{29\sqrt{59}\sqrt{1711}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Iffattura 1711=59\times 29. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{59\times 29} bħala l-prodott tal-għeruq kwadrati \sqrt{59}\sqrt{29}.

$$\frac{29\sqrt{59}\sqrt{59}\sqrt{29}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Immultiplika \sqrt{59} u \sqrt{59} biex tikseb 59.

$$\frac{29\times 59\sqrt{29}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Immultiplika 29 u 59 biex tikseb 1711.

$$\frac{1711\sqrt{29}-29\sqrt{59}\sqrt{145}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Biex timmultiplika \sqrt{59} u \sqrt{145}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-\sqrt{145}\sqrt{1711}+\left(\sqrt{145}\right)^{2}}{1566}$$

Biex timmultiplika \sqrt{145} u \sqrt{1711}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-\sqrt{248095}+\left(\sqrt{145}\right)^{2}}{1566}$$

Il-kwadrat ta' \sqrt{145} huwa 145.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-\sqrt{248095}+145}{1566}$$

Iffattura 248095=29^{2}\times 295. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{29^{2}\times 295} bħala l-prodott tal-għeruq kwadrati \sqrt{29^{2}}\sqrt{295}. Ħu l-għerq kwadrat ta' 29^{2}.

$$\frac{1711\sqrt{29}-29\sqrt{8555}-29\sqrt{295}+145}{1566}$$