6/sqrt{72}+8/sqrt{32} eching

$$\frac{ 6 }{ \sqrt{ 72 } } + \frac{ 8 }{ \sqrt{ 32 } }$$

Baholash

$$\frac{3\sqrt{2}}{2}\approx 2,121320344$$

Yechim qadamlari

Faktor: 72=6^{2}\times 2. \sqrt{6^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{6^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 6^{2} ning kvadrat ildizini chiqarish.

$$\frac{6}{6\sqrt{2}}+\frac{8}{\sqrt{32}}$$

\frac{6}{6\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{6\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}+\frac{8}{\sqrt{32}}$$

\sqrt{2} kvadrati – 2.

$$\frac{6\sqrt{2}}{6\times 2}+\frac{8}{\sqrt{32}}$$

Surat va maxrajdagi ikkala 6 ni qisqartiring.

$$\frac{\sqrt{2}}{2}+\frac{8}{\sqrt{32}}$$

Faktor: 32=4^{2}\times 2. \sqrt{4^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{2}}{2}+\frac{8}{4\sqrt{2}}$$

\frac{8}{4\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

$$\frac{\sqrt{2}}{2}+\frac{8\sqrt{2}}{4\times 2}$$

Surat va maxrajdagi ikkala 2\times 4 ni qisqartiring.

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

\frac{3}{2}\sqrt{2} ni olish uchun \frac{\sqrt{2}}{2} va \sqrt{2} ni birlashtirish.

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