sqrt{32}+sqrt{05}-2sqrt{1/3}-sqrt{1/8}+sqrt{12}-sqrt{18} eching

$$\sqrt{ 32 } + \sqrt{ 05 } -2 \sqrt{ \frac{ 1 }{ 3 } } - \sqrt{ \frac{ 1 }{ 8 } } + \sqrt{ 12 } - \sqrt{ 18 }$$

Baholash

$$\frac{3\sqrt{2}}{4}+\frac{4\sqrt{3}}{3}\approx 3,370061249$$

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.

$$4\sqrt{2}+\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+\sqrt{0}-2\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0-2\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0-2\times \frac{1}{\sqrt{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

\sqrt{3} kvadrati – 3.

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{3}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

\sqrt{\frac{1}{8}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{8}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{1}}{\sqrt{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{1}{\sqrt{8}}+\sqrt{12}-\sqrt{18}$$

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.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{1}{2\sqrt{2}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{12}-\sqrt{18}$$

\sqrt{2} kvadrati – 2.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{2\times 2}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}+\sqrt{12}-\sqrt{18}$$

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.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}+2\sqrt{3}-\sqrt{18}$$

Faktor: 18=3^{2}\times 2. \sqrt{3^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

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

\sqrt{2} ni olish uchun 4\sqrt{2} va -3\sqrt{2} ni birlashtirish.

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

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

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

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

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

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

$$\frac{3\sqrt{2}+6\sqrt{3}-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}$$

3\sqrt{2}+6\sqrt{3}-2\sqrt{3} hisob-kitobini qiling.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 4 ning eng kichik umumiy karralisi 12. \frac{3\sqrt{2}+4\sqrt{3}}{3} ni \frac{4}{4} marotabaga ko'paytirish. \frac{\sqrt{2}}{4} ni \frac{3}{3} marotabaga ko'paytirish.

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

\frac{4\left(3\sqrt{2}+4\sqrt{3}\right)}{12} va \frac{3\sqrt{2}}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

$$\frac{12\sqrt{2}+16\sqrt{3}-3\sqrt{2}}{12}$$

12\sqrt{2}+16\sqrt{3}-3\sqrt{2} hisob-kitobini qiling.

$$\frac{9\sqrt{2}+16\sqrt{3}}{12}$$