1/4sqrt{80}-1/6sqrt{63}-1/9sqrt{180} eching

$$\frac{ 1 }{ 4 } \sqrt{ 80 } - \frac{ 1 }{ 6 } \sqrt{ 63 } - \frac{ 1 }{ 9 } \sqrt{ 180 }$$

Baholash

$$\frac{\sqrt{5}}{3}-\frac{\sqrt{7}}{2}\approx -0,577519663$$

Yechim qadamlari

Faktor: 80=4^{2}\times 5. \sqrt{4^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$\frac{1}{4}\times 4\sqrt{5}-\frac{1}{6}\sqrt{63}-\frac{1}{9}\sqrt{180}$$

4 va 4 ni qisqartiring.

$$\sqrt{5}-\frac{1}{6}\sqrt{63}-\frac{1}{9}\sqrt{180}$$

Faktor: 63=3^{2}\times 7. \sqrt{3^{2}\times 7} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{7} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\sqrt{5}-\frac{1}{6}\times 3\sqrt{7}-\frac{1}{9}\sqrt{180}$$

-\frac{1}{6}\times 3 ni yagona kasrga aylantiring.

$$\sqrt{5}+\frac{-3}{6}\sqrt{7}-\frac{1}{9}\sqrt{180}$$

\frac{-3}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{5}-\frac{1}{2}\sqrt{7}-\frac{1}{9}\sqrt{180}$$

Faktor: 180=6^{2}\times 5. \sqrt{6^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{6^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 6^{2} ning kvadrat ildizini chiqarish.

$$\sqrt{5}-\frac{1}{2}\sqrt{7}-\frac{1}{9}\times 6\sqrt{5}$$

-\frac{1}{9}\times 6 ni yagona kasrga aylantiring.

$$\sqrt{5}-\frac{1}{2}\sqrt{7}+\frac{-6}{9}\sqrt{5}$$

\frac{-6}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{5}-\frac{1}{2}\sqrt{7}-\frac{2}{3}\sqrt{5}$$

\frac{1}{3}\sqrt{5} ni olish uchun \sqrt{5} va -\frac{2}{3}\sqrt{5} ni birlashtirish.

$$\frac{1}{3}\sqrt{5}-\frac{1}{2}\sqrt{7}$$

Omil

$$\frac{2 \sqrt{5} - 3 \sqrt{7}}{6} = -0,5775196630323655$$