1/sqrt{{left(frac{1{2}right)}^3}}-3/sqrt{frac{1{2}}} eching

$$\frac{ 1 }{ \sqrt{ { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } } } - \frac{ 3 }{ \sqrt{ \frac{ 1 }{ 2 } } }$$

Baholash

$$-\sqrt{2}\approx -1,414213562$$

Yechim qadamlari

3 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{8} ni qiymatni oling.

$$\frac{1}{\sqrt{\frac{1}{8}}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

\sqrt{\frac{1}{8}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{8}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{1}{\frac{\sqrt{1}}{\sqrt{8}}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$\frac{1}{\frac{1}{\sqrt{8}}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{1}{\frac{1}{2\sqrt{2}}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

\frac{1}{2\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{1}{\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

\sqrt{2} kvadrati – 2.

$$\frac{1}{\frac{\sqrt{2}}{2\times 2}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$\frac{1}{\frac{\sqrt{2}}{4}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

1 ni \frac{\sqrt{2}}{4} ga bo'lish 1 ga k'paytirish \frac{\sqrt{2}}{4} ga qaytarish.

$$\frac{4}{\sqrt{2}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

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

$$\frac{4\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{3}{\sqrt{\frac{1}{2}}}$$

\sqrt{2} kvadrati – 2.

$$\frac{4\sqrt{2}}{2}-\frac{3}{\sqrt{\frac{1}{2}}}$$

2\sqrt{2} ni olish uchun 4\sqrt{2} ni 2 ga bo‘ling.

$$2\sqrt{2}-\frac{3}{\sqrt{\frac{1}{2}}}$$

\sqrt{\frac{1}{2}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{2}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$2\sqrt{2}-\frac{3}{\frac{\sqrt{1}}{\sqrt{2}}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$2\sqrt{2}-\frac{3}{\frac{1}{\sqrt{2}}}$$

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

3 ni \frac{\sqrt{2}}{2} ga bo'lish 3 ga k'paytirish \frac{\sqrt{2}}{2} ga qaytarish.

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

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

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

\sqrt{2} kvadrati – 2.

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

6 hosil qilish uchun 3 va 2 ni ko'paytirish.

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

3\sqrt{2} ni olish uchun 6\sqrt{2} ni 2 ga bo‘ling.

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

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

$$-\sqrt{2}$$