sqrt{32}-sqrt{75}-sqrt{05}-2sqrt{1/3}= eching

$$\sqrt { 32 } - \sqrt { 75 } - \sqrt { 05 } - 2 \sqrt { \frac { 1 } { 3 } } =$$

Baholash

$$-\frac{17\sqrt{3}}{3}+4\sqrt{2}\approx -4,158100327$$

Qisqa yechim qadamlari

Faktor: 32=4^{2}\times 2. \sqrt{4^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$4\sqrt{2}-\sqrt{75}-\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}$$

Faktor: 75=5^{2}\times 3. \sqrt{5^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$4\sqrt{2}-5\sqrt{3}-\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}$$

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$4\sqrt{2}-5\sqrt{3}-\sqrt{0}-2\sqrt{\frac{1}{3}}$$

0 ning kvadrat ildizini hisoblab, 0 natijaga ega bo‘ling.

$$4\sqrt{2}-5\sqrt{3}-0-2\sqrt{\frac{1}{3}}$$

0 hosil qilish uchun -1 va 0 ni ko'paytirish.

$$4\sqrt{2}-5\sqrt{3}+0-2\sqrt{\frac{1}{3}}$$

\sqrt{\frac{1}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{1}{\sqrt{3}}$$

\frac{1}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{3}}{3}$$

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

$$4\sqrt{2}-5\sqrt{3}+0+\frac{-2\sqrt{3}}{3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4\sqrt{2}-5\sqrt{3}+0 ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)}{3}+\frac{-2\sqrt{3}}{3}$$

\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)}{3} va \frac{-2\sqrt{3}}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)-2\sqrt{3}}{3}$$

3\left(4\sqrt{2}-5\sqrt{3}+0\right)-2\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{12\sqrt{2}-15\sqrt{3}-2\sqrt{3}}{3}$$

12\sqrt{2}-15\sqrt{3}-2\sqrt{3} hisob-kitobini qiling.

$$\frac{12\sqrt{2}-17\sqrt{3}}{3}$$