1/2sqrt{3}divsqrt{1/12}*sqrt{27} eching

$$\frac { 1 } { 2 } \sqrt { 3 } \div \sqrt { \frac { 1 } { 12 } } \times \sqrt { 27 }$$

Baholash

$$9\sqrt{3}\approx 15,588457268$$

Yechim qadamlari

\sqrt{\frac{1}{12}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{12}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{1}{2}\sqrt{3}}{\frac{\sqrt{1}}{\sqrt{12}}}\sqrt{27}$$

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

$$\frac{\frac{1}{2}\sqrt{3}}{\frac{1}{\sqrt{12}}}\sqrt{27}$$

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{1}{2}\sqrt{3}}{\frac{1}{2\sqrt{3}}}\sqrt{27}$$

\frac{1}{2\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{1}{2}\sqrt{3}}{\frac{\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}}\sqrt{27}$$

\sqrt{3} kvadrati – 3.

$$\frac{\frac{1}{2}\sqrt{3}}{\frac{\sqrt{3}}{2\times 3}}\sqrt{27}$$

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

$$\frac{\frac{1}{2}\sqrt{3}}{\frac{\sqrt{3}}{6}}\sqrt{27}$$

\frac{1}{2}\sqrt{3} ni \frac{\sqrt{3}}{6} ga bo'lish \frac{1}{2}\sqrt{3} ga k'paytirish \frac{\sqrt{3}}{6} ga qaytarish.

$$\frac{\frac{1}{2}\sqrt{3}\times 6}{\sqrt{3}}\sqrt{27}$$

\frac{\frac{1}{2}\sqrt{3}\times 6}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{1}{2}\sqrt{3}\times 6\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{27}$$

\sqrt{3} kvadrati – 3.

$$\frac{\frac{1}{2}\sqrt{3}\times 6\sqrt{3}}{3}\sqrt{27}$$

\frac{6}{2} hosil qilish uchun \frac{1}{2} va 6 ni ko'paytirish.

$$\frac{\frac{6}{2}\sqrt{3}\sqrt{3}}{3}\sqrt{27}$$

3 ni olish uchun 6 ni 2 ga bo‘ling.

$$\frac{3\sqrt{3}\sqrt{3}}{3}\sqrt{27}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$\frac{3\times 3}{3}\sqrt{27}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$\frac{9}{3}\sqrt{27}$$

3 ni olish uchun 9 ni 3 ga bo‘ling.

$$3\sqrt{27}$$

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.

$$3\times 3\sqrt{3}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$9\sqrt{3}$$