frac{sqrt[3]{27}+sqrt{27}-sqrt{48}}{2-sqrt{2}} eching

$$\frac { \sqrt[ 3 ] { 27 } + \sqrt { 27 } - \sqrt { 48 } } { 2 - \sqrt { 2 } }$$

Baholash

$$\frac{3\sqrt{2}}{2}-\frac{\sqrt{6}}{2}+3-\sqrt{3}\approx 2,164524665$$

Yechim qadamlari

\sqrt[3]{27} ni hisoblab, 3 natijasiga ega bo‘ling.

$$\frac{3+\sqrt{27}-\sqrt{48}}{2-\sqrt{2}}$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{3+3\sqrt{3}-\sqrt{48}}{2-\sqrt{2}}$$

Faktor: 48=4^{2}\times 3. \sqrt{4^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$\frac{3+3\sqrt{3}-4\sqrt{3}}{2-\sqrt{2}}$$

-\sqrt{3} ni olish uchun 3\sqrt{3} va -4\sqrt{3} ni birlashtirish.

$$\frac{3-\sqrt{3}}{2-\sqrt{2}}$$

\frac{3-\sqrt{3}}{2-\sqrt{2}} maxrajini 2+\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(3-\sqrt{3}\right)\left(2+\sqrt{2}\right)}{\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)}$$

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

$$\frac{\left(3-\sqrt{3}\right)\left(2+\sqrt{2}\right)}{2^{2}-\left(\sqrt{2}\right)^{2}}$$

2 kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

$$\frac{\left(3-\sqrt{3}\right)\left(2+\sqrt{2}\right)}{4-2}$$

2 olish uchun 4 dan 2 ni ayirish.

$$\frac{\left(3-\sqrt{3}\right)\left(2+\sqrt{2}\right)}{2}$$

3-\sqrt{3} ga 2+\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{6+3\sqrt{2}-2\sqrt{3}-\sqrt{3}\sqrt{2}}{2}$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{6+3\sqrt{2}-2\sqrt{3}-\sqrt{6}}{2}$$