sqrt{1div2+1div4+1div8+1div16} eching

$$\sqrt{ 1 \div 2+1 \div 4+1 \div 8+1 \div 16 }$$

Baholash

$$\frac{\sqrt{15}}{4}\approx 0,968245837$$

Yechim qadamlari

2 va 4 ning eng kichik umumiy karralisi 4 ga teng. \frac{1}{2} va \frac{1}{4} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{2}{4}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}}$$

\frac{2}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{2+1}{4}+\frac{1}{8}+\frac{1}{16}}$$

3 olish uchun 2 va 1'ni qo'shing.

$$\sqrt{\frac{3}{4}+\frac{1}{8}+\frac{1}{16}}$$

4 va 8 ning eng kichik umumiy karralisi 8 ga teng. \frac{3}{4} va \frac{1}{8} ni 8 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{6}{8}+\frac{1}{8}+\frac{1}{16}}$$

\frac{6}{8} va \frac{1}{8} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{6+1}{8}+\frac{1}{16}}$$

7 olish uchun 6 va 1'ni qo'shing.

$$\sqrt{\frac{7}{8}+\frac{1}{16}}$$

8 va 16 ning eng kichik umumiy karralisi 16 ga teng. \frac{7}{8} va \frac{1}{16} ni 16 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{14}{16}+\frac{1}{16}}$$

\frac{14}{16} va \frac{1}{16} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{14+1}{16}}$$

15 olish uchun 14 va 1'ni qo'shing.

$$\sqrt{\frac{15}{16}}$$

\sqrt{\frac{15}{16}} boʻlinmasining kvadrat ildizini \frac{\sqrt{15}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{15}}{\sqrt{16}}$$

16 ning kvadrat ildizini hisoblab, 4 natijaga ega bo‘ling.

$$\frac{\sqrt{15}}{4}$$