sqrt{{[(2/3+1/2)-1/6]^2}^3+1-(2/3+frac{7}{6}+frac{2}{12})+[15*(frac{1}{3}+frac{1}{5})]^2} eching

$$\sqrt { \{ [ ( \frac { 2 } { 3 } + \frac { 1 } { 2 } ) - \frac { 1 } { 6 } ] ^ { 2 } \} ^ { 3 } + 1 - ( \frac { 2 } { 3 } + \frac { 7 } { 6 } + \frac { 2 } { 12 } ) + [ 15 \times ( \frac { 1 } { 3 } + \frac { 1 } { 5 } ) ] ^ { 2 } }$$

Baholash

$$8$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 3 ni ko‘paytirib, 6 ni oling.

$$\sqrt{\left(\frac{2}{3}+\frac{1}{2}-\frac{1}{6}\right)^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

\frac{7}{6} olish uchun \frac{2}{3} va \frac{1}{2}'ni qo'shing.

$$\sqrt{\left(\frac{7}{6}-\frac{1}{6}\right)^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

1 olish uchun \frac{7}{6} dan \frac{1}{6} ni ayirish.

$$\sqrt{1^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

6 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\sqrt{1+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

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

$$\sqrt{2-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

\frac{11}{6} olish uchun \frac{2}{3} va \frac{7}{6}'ni qo'shing.

$$\sqrt{2-\left(\frac{11}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

\frac{2}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{2-\left(\frac{11}{6}+\frac{1}{6}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

2 olish uchun \frac{11}{6} va \frac{1}{6}'ni qo'shing.

$$\sqrt{2-2+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

0 olish uchun 2 dan 2 ni ayirish.

$$\sqrt{0+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

\frac{8}{15} olish uchun \frac{1}{3} va \frac{1}{5}'ni qo'shing.

$$\sqrt{0+\left(15\times \frac{8}{15}\right)^{2}}$$

8 hosil qilish uchun 15 va \frac{8}{15} ni ko'paytirish.

$$\sqrt{0+8^{2}}$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$\sqrt{0+64}$$

64 olish uchun 0 va 64'ni qo'shing.

$$\sqrt{64}$$

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

$$8$$

Omil

$$2^{3}$$