-{[(1/sqrt{2})-(-1/sqrt{5})]+(-sqrt{4})^3+2(sqrt{16}-1/2)}div(3/4) eching

$$- \{ [ ( \frac { 1 } { \sqrt { 2 } } ) - ( - \frac { 1 } { \sqrt { 5 } } ) ] + ( - \sqrt { 4 } ) ^ { 3 } + 2 ( \sqrt { 16 } - \frac { 1 } { 2 } ) \} \div ( \frac { 3 } { 4 } )$$

Baholash

$$-\frac{2\sqrt{2}}{3}-\frac{4\sqrt{5}}{15}+\frac{4}{3}\approx -0,205760502$$

Qisqa yechim qadamlari

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{-\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\left(-\frac{1}{\sqrt{5}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

\sqrt{2} kvadrati – 2.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{1}{\sqrt{5}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

\frac{1}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

\sqrt{5} kvadrati – 5.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)+\left(-2\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

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

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

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

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\left(4-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

\frac{7}{2} olish uchun 4 dan \frac{1}{2} ni ayirish.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+2\times \frac{7}{2}\right)}{\frac{3}{4}}$$

7 hosil qilish uchun 2 va \frac{7}{2} ni ko'paytirish.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-8+7\right)}{\frac{3}{4}}$$

-1 olish uchun -8 va 7'ni qo'shing.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-1\right)}{\frac{3}{4}}$$

\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)-1 teskarisini topish uchun har birining teskarisini toping.

$$\frac{-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1}{\frac{3}{4}}$$

-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1 ni \frac{3}{4} ga bo'lish -\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1 ga k'paytirish \frac{3}{4} ga qaytarish.

$$\frac{\left(-\left(\frac{\sqrt{2}}{2}-\left(-\frac{\sqrt{5}}{5}\right)\right)+1\right)\times 4}{3}$$

1 hosil qilish uchun -1 va -1 ni ko'paytirish.

$$\frac{\left(-\left(\frac{\sqrt{2}}{2}+\frac{\sqrt{5}}{5}\right)+1\right)\times 4}{3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va 5 ning eng kichik umumiy karralisi 10. \frac{\sqrt{2}}{2} ni \frac{5}{5} marotabaga ko'paytirish. \frac{\sqrt{5}}{5} ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{\left(-\left(\frac{5\sqrt{2}}{10}+\frac{2\sqrt{5}}{10}\right)+1\right)\times 4}{3}$$

\frac{5\sqrt{2}}{10} va \frac{2\sqrt{5}}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(-\frac{5\sqrt{2}+2\sqrt{5}}{10}+1\right)\times 4}{3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{10}{10} marotabaga ko'paytirish.

$$\frac{\left(-\frac{5\sqrt{2}+2\sqrt{5}}{10}+\frac{10}{10}\right)\times 4}{3}$$

-\frac{5\sqrt{2}+2\sqrt{5}}{10} va \frac{10}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-\left(5\sqrt{2}+2\sqrt{5}\right)+10}{10}\times 4}{3}$$

-\left(5\sqrt{2}+2\sqrt{5}\right)+10 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{-5\sqrt{2}-2\sqrt{5}+10}{10}\times 4}{3}$$

\frac{-5\sqrt{2}-2\sqrt{5}+10}{10}\times 4 ni yagona kasrga aylantiring.

$$\frac{\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10}}{3}$$

\frac{\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10}}{3} ni yagona kasrga aylantiring.

$$\frac{\left(-5\sqrt{2}-2\sqrt{5}+10\right)\times 4}{10\times 3}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{2\left(-5\sqrt{2}-2\sqrt{5}+10\right)}{3\times 5}$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\frac{2\left(-5\sqrt{2}-2\sqrt{5}+10\right)}{15}$$

2 ga -5\sqrt{2}-2\sqrt{5}+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{-10\sqrt{2}-4\sqrt{5}+20}{15}$$