5sqrt{25^2-7^2/27} eching

$$5 \sqrt { \frac { 25 ^ { 2 } - 7 ^ { 2 } } { 27 } }$$

Baholash

$$\frac{40\sqrt{3}}{3}\approx 23,094010768$$

Yechim qadamlari

2 daraja ko‘rsatkichini 25 ga hisoblang va 625 ni qiymatni oling.

$$5\sqrt{\frac{625-7^{2}}{27}}$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$5\sqrt{\frac{625-49}{27}}$$

576 olish uchun 625 dan 49 ni ayirish.

$$5\sqrt{\frac{576}{27}}$$

\frac{576}{27} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$5\sqrt{\frac{64}{3}}$$

\sqrt{\frac{64}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{64}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$5\times \frac{\sqrt{64}}{\sqrt{3}}$$

64 ning kvadrat ildizini hisoblab, 8 natijaga ega bo‘ling.

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

\frac{8}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$5\times \frac{8\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

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

5\times \frac{8\sqrt{3}}{3} ni yagona kasrga aylantiring.

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

40 hosil qilish uchun 5 va 8 ni ko'paytirish.

$$\frac{40\sqrt{3}}{3}$$