(sqrt{8}-2sqrt{025)}-(sqrt{11/8}+sqrt{50}+2/3sqrt{12}) eching

$$( \sqrt { 8 } - 2 \sqrt { 025 ) } - ( \sqrt { 1 \frac { 1 } { 8 } } + \sqrt { 50 } + \frac { 2 } { 3 } \sqrt { 12 } )$$

Baholash

$$-\frac{4\sqrt{3}}{3}-\frac{15\sqrt{2}}{4}-10\approx -17,612701936$$

Yechim qadamlari

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.

$$2\sqrt{2}-2\sqrt{25}-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

25 ning kvadrat ildizini hisoblab, 5 natijaga ega bo‘ling.

$$2\sqrt{2}-2\times 5-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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

$$2\sqrt{2}-10-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

8 hosil qilish uchun 1 va 8 ni ko'paytirish.

$$2\sqrt{2}-10-\left(\sqrt{\frac{8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

9 olish uchun 8 va 1'ni qo'shing.

$$2\sqrt{2}-10-\left(\sqrt{\frac{9}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

\sqrt{\frac{9}{8}} boʻlinmasining kvadrat ildizini \frac{\sqrt{9}}{\sqrt{8}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$2\sqrt{2}-10-\left(\frac{\sqrt{9}}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

$$2\sqrt{2}-10-\left(\frac{3}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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.

$$2\sqrt{2}-10-\left(\frac{3}{2\sqrt{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

\frac{3}{2\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

\sqrt{2} kvadrati – 2.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\times 2}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Faktor: 50=5^{2}\times 2. \sqrt{5^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+5\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

\frac{23}{4}\sqrt{2} ni olish uchun \frac{3\sqrt{2}}{4} va 5\sqrt{2} ni birlashtirish.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\times 2\sqrt{3}\right)$$

\frac{2}{3}\times 2 ni yagona kasrga aylantiring.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2\times 2}{3}\sqrt{3}\right)$$

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

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}\right)$$

\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3} teskarisini topish uchun har birining teskarisini toping.

$$2\sqrt{2}-10-\frac{23}{4}\sqrt{2}-\frac{4}{3}\sqrt{3}$$

-\frac{15}{4}\sqrt{2} ni olish uchun 2\sqrt{2} va -\frac{23}{4}\sqrt{2} ni birlashtirish.

$$-\frac{15}{4}\sqrt{2}-10-\frac{4}{3}\sqrt{3}$$

Omil

$$\frac{-16 \sqrt{3} - 45 \sqrt{2} - 120}{12} = -17,612701935657608$$