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

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

Arvuta

$$\frac{59\sqrt{29}+5-\sqrt{295}-\sqrt{8555}}{54}\approx 3,945479937$$

Lahenduse etapid

Korrutage 5 ja 29, et leida 145.

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

Korrutage 59 ja 29, et leida 1711.

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

Korrutage 5 ja 29, et leida 145.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{1711}-\sqrt{145} nimetaja \frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{145}} nimetaja.

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

Mõelge valemile \left(\sqrt{1711}+\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Tõstke \sqrt{1711} ruutu. Tõstke \sqrt{145} ruutu.

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

Lahutage 145 väärtusest 1711, et leida 1566.

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

Rakendage distributiivsusomadus, korrutades avaldise 29\sqrt{59}-\sqrt{145} iga liikme avaldise \sqrt{1711}-\sqrt{145} iga liikmega.

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

Tegurda 1711=59\times 29. Kirjutage \sqrt{59\times 29} toote juured, kui see ruut \sqrt{59}\sqrt{29}.

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

Korrutage \sqrt{59} ja \sqrt{59}, et leida 59.

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

Korrutage 29 ja 59, et leida 1711.

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

\sqrt{59} ja \sqrt{145} korrutage numbrid, mis on sama juur.

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

\sqrt{145} ja \sqrt{1711} korrutage numbrid, mis on sama juur.

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

\sqrt{145} ruut on 145.

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

Tegurda 248095=29^{2}\times 295. Kirjutage \sqrt{29^{2}\times 295} toote juured, kui see ruut \sqrt{29^{2}}\sqrt{295}. Leidke 29^{2} ruutjuur.

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