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

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

Baholash

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

Yechim qadamlari

145 hosil qilish uchun 5 va 29 ni ko'paytirish.

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

1711 hosil qilish uchun 59 va 29 ni ko'paytirish.

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

145 hosil qilish uchun 5 va 29 ni ko'paytirish.

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

\frac{29\sqrt{59}-\sqrt{145}}{\sqrt{1711}+\sqrt{145}} maxrajini \sqrt{1711}-\sqrt{145} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(\sqrt{1711}+\sqrt{145}\right)\left(\sqrt{1711}-\sqrt{145}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\sqrt{1711} kvadratini chiqarish. \sqrt{145} kvadratini chiqarish.

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

1566 olish uchun 1711 dan 145 ni ayirish.

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

29\sqrt{59}-\sqrt{145} ifodaning har bir elementini \sqrt{1711}-\sqrt{145} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

Faktor: 1711=59\times 29. \sqrt{59\times 29} koʻpaytmasining kvadrat ildizini \sqrt{59}\sqrt{29} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

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

59 hosil qilish uchun \sqrt{59} va \sqrt{59} ni ko'paytirish.

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

1711 hosil qilish uchun 29 va 59 ni ko'paytirish.

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

\sqrt{59} va \sqrt{145} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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

\sqrt{145} va \sqrt{1711} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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

\sqrt{145} kvadrati – 145.

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

Faktor: 248095=29^{2}\times 295. \sqrt{29^{2}\times 295} koʻpaytmasining kvadrat ildizini \sqrt{29^{2}}\sqrt{295} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 29^{2} ning kvadrat ildizini chiqarish.

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