1/sqrt{2008-sqrt{200}} eching

$$\frac { 1 } { \sqrt { 2008 } - \sqrt { 200 } }$$

Baholash

$$\frac{\sqrt{502}+5\sqrt{2}}{904}\approx 0,032606664$$

Yechim qadamlari

Faktor: 2008=2^{2}\times 502. \sqrt{2^{2}\times 502} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{502} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{1}{2\sqrt{502}-\sqrt{200}}$$

Faktor: 200=10^{2}\times 2. \sqrt{10^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{10^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 10^{2} ning kvadrat ildizini chiqarish.

$$\frac{1}{2\sqrt{502}-10\sqrt{2}}$$

\frac{1}{2\sqrt{502}-10\sqrt{2}} maxrajini 2\sqrt{502}+10\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{502}+10\sqrt{2}}{\left(2\sqrt{502}-10\sqrt{2}\right)\left(2\sqrt{502}+10\sqrt{2}\right)}$$

Hisoblang: \left(2\sqrt{502}-10\sqrt{2}\right)\left(2\sqrt{502}+10\sqrt{2}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\sqrt{502}+10\sqrt{2}}{\left(2\sqrt{502}\right)^{2}-\left(-10\sqrt{2}\right)^{2}}$$

\left(2\sqrt{502}\right)^{2} ni kengaytirish.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2^{2}\left(\sqrt{502}\right)^{2}-\left(-10\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{2\sqrt{502}+10\sqrt{2}}{4\left(\sqrt{502}\right)^{2}-\left(-10\sqrt{2}\right)^{2}}$$

\sqrt{502} kvadrati – 502.

$$\frac{2\sqrt{502}+10\sqrt{2}}{4\times 502-\left(-10\sqrt{2}\right)^{2}}$$

2008 hosil qilish uchun 4 va 502 ni ko'paytirish.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-\left(-10\sqrt{2}\right)^{2}}$$

\left(-10\sqrt{2}\right)^{2} ni kengaytirish.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-\left(-10\right)^{2}\left(\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini -10 ga hisoblang va 100 ni qiymatni oling.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-100\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-100\times 2}$$

200 hosil qilish uchun 100 va 2 ni ko'paytirish.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-200}$$

1808 olish uchun 2008 dan 200 ni ayirish.

$$\frac{2\sqrt{502}+10\sqrt{2}}{1808}$$