17+1/72+16sqrt{8}+2/3+1/4 eching

$$17 + \frac { 1 } { 72 } + 16 \sqrt { 8 } + \frac { 2 } { 3 } + \frac { 1 } { 4 }$$

Baholash

$$32\sqrt{2}+\frac{1291}{72}\approx 63,185389551$$

Yechim qadamlari

17 ni \frac{1224}{72} kasrga o‘giring.

$$\frac{1224}{72}+\frac{1}{72}+16\sqrt{8}+\frac{2}{3}+\frac{1}{4}$$

\frac{1224}{72} va \frac{1}{72} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1224+1}{72}+16\sqrt{8}+\frac{2}{3}+\frac{1}{4}$$

1225 olish uchun 1224 va 1'ni qo'shing.

$$\frac{1225}{72}+16\sqrt{8}+\frac{2}{3}+\frac{1}{4}$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{1225}{72}+16\times 2\sqrt{2}+\frac{2}{3}+\frac{1}{4}$$

32 hosil qilish uchun 16 va 2 ni ko'paytirish.

$$\frac{1225}{72}+32\sqrt{2}+\frac{2}{3}+\frac{1}{4}$$

72 va 3 ning eng kichik umumiy karralisi 72 ga teng. \frac{1225}{72} va \frac{2}{3} ni 72 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1225}{72}+32\sqrt{2}+\frac{48}{72}+\frac{1}{4}$$

\frac{1225}{72} va \frac{48}{72} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1225+48}{72}+32\sqrt{2}+\frac{1}{4}$$

1273 olish uchun 1225 va 48'ni qo'shing.

$$\frac{1273}{72}+32\sqrt{2}+\frac{1}{4}$$

72 va 4 ning eng kichik umumiy karralisi 72 ga teng. \frac{1273}{72} va \frac{1}{4} ni 72 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1273}{72}+32\sqrt{2}+\frac{18}{72}$$

\frac{1273}{72} va \frac{18}{72} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1273+18}{72}+32\sqrt{2}$$

1291 olish uchun 1273 va 18'ni qo'shing.

$$\frac{1291}{72}+32\sqrt{2}$$

Omil

$$\frac{2304 \sqrt{2} + 1291}{72} = 63,18538955149461$$