1/4sqrt{80}-1/16sqrt{63}-1/9sqrt{180} eching

$$\frac { 1 } { 4 } \sqrt { 80 } - \frac { 1 } { 16 } \sqrt { 63 } - \frac { 1 } { 9 } \sqrt { 180 }$$

Baholash

$$\frac{\sqrt{5}}{3}-\frac{3\sqrt{7}}{16}\approx 0,249277622$$

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.

$$\frac{1}{4}\times 4\sqrt{5}-\frac{1}{16}\sqrt{63}-\frac{1}{9}\sqrt{180}$$

4 va 4 ni qisqartiring.

$$\sqrt{5}-\frac{1}{16}\sqrt{63}-\frac{1}{9}\sqrt{180}$$

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.

$$\sqrt{5}-\frac{1}{16}\times 3\sqrt{7}-\frac{1}{9}\sqrt{180}$$

-\frac{1}{16}\times 3 ni yagona kasrga aylantiring.

$$\sqrt{5}+\frac{-3}{16}\sqrt{7}-\frac{1}{9}\sqrt{180}$$

\frac{-3}{16} kasri manfiy belgini olib tashlash bilan -\frac{3}{16} sifatida qayta yozilishi mumkin.

$$\sqrt{5}-\frac{3}{16}\sqrt{7}-\frac{1}{9}\sqrt{180}$$

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.

$$\sqrt{5}-\frac{3}{16}\sqrt{7}-\frac{1}{9}\times 6\sqrt{5}$$

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

$$\sqrt{5}-\frac{3}{16}\sqrt{7}+\frac{-6}{9}\sqrt{5}$$

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

$$\sqrt{5}-\frac{3}{16}\sqrt{7}-\frac{2}{3}\sqrt{5}$$

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

$$\frac{1}{3}\sqrt{5}-\frac{3}{16}\sqrt{7}$$

Omil

$$\frac{16 \sqrt{5} - 9 \sqrt{7}}{48} = 0,2492776216753192$$