2/2-(1/6sqrt{24}-3/8sqrt{12}) eching

$$\frac { 2 } { 2 } - ( \frac { 1 } { 6 } \sqrt { 24 } - \frac { 3 } { 8 } \sqrt { 12 } )$$

Baholash

$$\frac{3\sqrt{3}}{4}-\frac{\sqrt{6}}{3}+1\approx 1,482541525$$

Yechim qadamlari

1 ni olish uchun 2 ni 2 ga bo‘ling.

$$1-\left(\frac{1}{6}\sqrt{24}-\frac{3}{8}\sqrt{12}\right)$$

Faktor: 24=2^{2}\times 6. \sqrt{2^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$1-\left(\frac{1}{6}\times 2\sqrt{6}-\frac{3}{8}\sqrt{12}\right)$$

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

$$1-\left(\frac{2}{6}\sqrt{6}-\frac{3}{8}\sqrt{12}\right)$$

\frac{2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$1-\left(\frac{1}{3}\sqrt{6}-\frac{3}{8}\sqrt{12}\right)$$

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.

$$1-\left(\frac{1}{3}\sqrt{6}-\frac{3}{8}\times 2\sqrt{3}\right)$$

-\frac{3}{8}\times 2 ni yagona kasrga aylantiring.

$$1-\left(\frac{1}{3}\sqrt{6}+\frac{-3\times 2}{8}\sqrt{3}\right)$$

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

$$1-\left(\frac{1}{3}\sqrt{6}+\frac{-6}{8}\sqrt{3}\right)$$

\frac{-6}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$1-\left(\frac{1}{3}\sqrt{6}-\frac{3}{4}\sqrt{3}\right)$$

\frac{1}{3}\sqrt{6}-\frac{3}{4}\sqrt{3} teskarisini topish uchun har birining teskarisini toping.

$$1-\frac{1}{3}\sqrt{6}-\left(-\frac{3}{4}\sqrt{3}\right)$$

-\frac{3}{4}\sqrt{3} ning teskarisi \frac{3}{4}\sqrt{3} ga teng.

$$1-\frac{1}{3}\sqrt{6}+\frac{3}{4}\sqrt{3}$$

Omil

$$\frac{9 \sqrt{3} + 12 - 4 \sqrt{6}}{12} = 1,482541524748932$$