2/sqrt{5}+sqrt{20}+8/sqrt{80} eching

$$\frac { 2 } { \sqrt { 5 } } + \sqrt { 20 } + \frac { 8 } { \sqrt { 80 } }$$

Baholash

$$\frac{14\sqrt{5}}{5}\approx 6,260990337$$

Yechim qadamlari

\frac{2}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\sqrt{20}+\frac{8}{\sqrt{80}}$$

\sqrt{5} kvadrati – 5.

$$\frac{2\sqrt{5}}{5}+\sqrt{20}+\frac{8}{\sqrt{80}}$$

Faktor: 20=2^{2}\times 5. \sqrt{2^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{2\sqrt{5}}{5}+2\sqrt{5}+\frac{8}{\sqrt{80}}$$

\frac{12}{5}\sqrt{5} ni olish uchun \frac{2\sqrt{5}}{5} va 2\sqrt{5} ni birlashtirish.

$$\frac{12}{5}\sqrt{5}+\frac{8}{\sqrt{80}}$$

Faktor: 80=4^{2}\times 5. \sqrt{4^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$\frac{12}{5}\sqrt{5}+\frac{8}{4\sqrt{5}}$$

\frac{8}{4\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{12}{5}\sqrt{5}+\frac{8\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{12}{5}\sqrt{5}+\frac{8\sqrt{5}}{4\times 5}$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{12}{5}\sqrt{5}+\frac{2\sqrt{5}}{5}$$

\frac{14}{5}\sqrt{5} ni olish uchun \frac{12}{5}\sqrt{5} va \frac{2\sqrt{5}}{5} ni birlashtirish.

$$\frac{14}{5}\sqrt{5}$$