sqrt{27}*3sqrt{12}*5/8sqrt{3} eching

$$\sqrt { 27 } \times 3 \sqrt { 12 } \times \frac { 5 } { 8 } \sqrt { 3 }$$

Baholash

$$\frac{135\sqrt{3}}{4}\approx 58,456714755$$

Yechim qadamlari

Faktor: 27=3\times 9. \sqrt{3\times 9} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{9} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$3\sqrt{3}\sqrt{9}\sqrt{12}\times \frac{5}{8}\sqrt{3}$$

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

$$3\times 3\sqrt{12}\times \frac{5}{8}\sqrt{9}$$

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

$$9\sqrt{12}\times \frac{5}{8}\sqrt{9}$$

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.

$$9\times 2\sqrt{3}\times \frac{5}{8}\sqrt{9}$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$18\sqrt{3}\times \frac{5}{8}\sqrt{9}$$

18\times \frac{5}{8} ni yagona kasrga aylantiring.

$$\frac{18\times 5}{8}\sqrt{3}\sqrt{9}$$

90 hosil qilish uchun 18 va 5 ni ko'paytirish.

$$\frac{90}{8}\sqrt{3}\sqrt{9}$$

\frac{90}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{45}{4}\sqrt{3}\sqrt{9}$$

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

$$\frac{45}{4}\sqrt{3}\times 3$$

\frac{45}{4}\times 3 ni yagona kasrga aylantiring.

$$\frac{45\times 3}{4}\sqrt{3}$$

135 hosil qilish uchun 45 va 3 ni ko'paytirish.

$$\frac{135}{4}\sqrt{3}$$