sqrt{[(21/2-1/6+0.2)*9]-11/4}= eching

$$\sqrt { [ ( 2 \frac { 1 } { 2 } - \frac { 1 } { 6 } + 0.2 ) \cdot 9 ] - \frac { 11 } { 4 } } =$$

Baholash

$$\frac{\sqrt{2005}}{10}\approx 4,477722635$$

Yechim qadamlari

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

$$\sqrt{\left(\frac{4+1}{2}-\frac{1}{6}+0,2\right)\times 9-\frac{11}{4}}$$

5 olish uchun 4 va 1'ni qo'shing.

$$\sqrt{\left(\frac{5}{2}-\frac{1}{6}+0,2\right)\times 9-\frac{11}{4}}$$

2 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{5}{2} va \frac{1}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\frac{15}{6}-\frac{1}{6}+0,2\right)\times 9-\frac{11}{4}}$$

\frac{15}{6} va \frac{1}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\left(\frac{15-1}{6}+0,2\right)\times 9-\frac{11}{4}}$$

14 olish uchun 15 dan 1 ni ayirish.

$$\sqrt{\left(\frac{14}{6}+0,2\right)\times 9-\frac{11}{4}}$$

\frac{14}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{7}{3}+0,2\right)\times 9-\frac{11}{4}}$$

0,2 o‘nlik raqamni uning \frac{2}{10} kasrga o‘giring. \frac{2}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{7}{3}+\frac{1}{5}\right)\times 9-\frac{11}{4}}$$

3 va 5 ning eng kichik umumiy karralisi 15 ga teng. \frac{7}{3} va \frac{1}{5} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\frac{35}{15}+\frac{3}{15}\right)\times 9-\frac{11}{4}}$$

\frac{35}{15} va \frac{3}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{35+3}{15}\times 9-\frac{11}{4}}$$

38 olish uchun 35 va 3'ni qo'shing.

$$\sqrt{\frac{38}{15}\times 9-\frac{11}{4}}$$

\frac{38}{15}\times 9 ni yagona kasrga aylantiring.

$$\sqrt{\frac{38\times 9}{15}-\frac{11}{4}}$$

342 hosil qilish uchun 38 va 9 ni ko'paytirish.

$$\sqrt{\frac{342}{15}-\frac{11}{4}}$$

\frac{342}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{114}{5}-\frac{11}{4}}$$

5 va 4 ning eng kichik umumiy karralisi 20 ga teng. \frac{114}{5} va \frac{11}{4} ni 20 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{456}{20}-\frac{55}{20}}$$

\frac{456}{20} va \frac{55}{20} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{456-55}{20}}$$

401 olish uchun 456 dan 55 ni ayirish.

$$\sqrt{\frac{401}{20}}$$

\sqrt{\frac{401}{20}} boʻlinmasining kvadrat ildizini \frac{\sqrt{401}}{\sqrt{20}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{401}}{\sqrt{20}}$$

Faktor: 20=2^{2}\times 5. \sqrt{2^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{401}}{2\sqrt{5}}$$

\frac{\sqrt{401}}{2\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{401}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{401}\sqrt{5}}{2\times 5}$$

\sqrt{401} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{2005}}{2\times 5}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$\frac{\sqrt{2005}}{10}$$