3/4sqrt{24}div9sqrt{2}*(2/3sqrt{32}) eching

$$\frac { 3 } { 4 } \sqrt { 24 } \div 9 \sqrt { 2 } \times ( \frac { 2 } { 3 } \sqrt { 32 } )$$

Baholash

$$\frac{8\sqrt{6}}{9}\approx 2,177324216$$

Yechim qadamlari

Faktor: 32=2\times 16. \sqrt{2\times 16} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{16} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{\frac{3}{4}\sqrt{24}}{9}\sqrt{2}\times \frac{2}{3}\sqrt{2}\sqrt{16}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$\frac{\frac{3}{4}\sqrt{24}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

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.

$$\frac{\frac{3}{4}\times 2\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

\frac{3}{4}\times 2 ni yagona kasrga aylantiring.

$$\frac{\frac{3\times 2}{4}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

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

$$\frac{\frac{6}{4}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

\frac{6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{3}{2}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

\frac{1}{6}\sqrt{6} ni olish uchun \frac{3}{2}\sqrt{6} ni 9 ga bo‘ling.

$$\frac{1}{6}\sqrt{6}\times 2\times \frac{2}{3}\sqrt{16}$$

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

$$\frac{2}{6}\sqrt{6}\times \frac{2}{3}\sqrt{16}$$

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

$$\frac{1}{3}\sqrt{6}\times \frac{2}{3}\sqrt{16}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{3} ni \frac{2}{3} ga ko‘paytiring.

$$\frac{1\times 2}{3\times 3}\sqrt{6}\sqrt{16}$$

\frac{1\times 2}{3\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\frac{2}{9}\sqrt{6}\sqrt{16}$$

16 ning kvadrat ildizini hisoblab, 4 natijaga ega bo‘ling.

$$\frac{2}{9}\sqrt{6}\times 4$$

\frac{2}{9}\times 4 ni yagona kasrga aylantiring.

$$\frac{2\times 4}{9}\sqrt{6}$$

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

$$\frac{8}{9}\sqrt{6}$$