(sqrt{27}-2/3sqrt{18})-(sqrt{4/3}-4sqrt{1/2}) eching

$$( \sqrt { 27 } - \frac { 2 } { 3 } \sqrt { 18 } ) - ( \sqrt { \frac { 4 } { 3 } } - 4 \sqrt { \frac { 1 } { 2 } } )$$

Baholash

$$\frac{7\sqrt{3}}{3}\approx 4,041451884$$

Qisqa yechim qadamlari

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$3\sqrt{3}-\frac{2}{3}\sqrt{18}-\left(\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}\right)$$

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.

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

3 va 3 ni qisqartiring.

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

\sqrt{\frac{4}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{4}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

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

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

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

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

\sqrt{3} kvadrati – 3.

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

\sqrt{\frac{1}{2}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{2}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

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

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

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

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

\sqrt{2} kvadrati – 2.

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

4 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

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

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

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

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

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

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

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

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

$$\frac{3\left(3\sqrt{3}-2\sqrt{2}\right)}{3}-\frac{2\sqrt{3}-6\sqrt{2}}{3}$$

\frac{3\left(3\sqrt{3}-2\sqrt{2}\right)}{3} va \frac{2\sqrt{3}-6\sqrt{2}}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3\left(3\sqrt{3}-2\sqrt{2}\right)-\left(2\sqrt{3}-6\sqrt{2}\right)}{3}$$

3\left(3\sqrt{3}-2\sqrt{2}\right)-\left(2\sqrt{3}-6\sqrt{2}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{9\sqrt{3}-6\sqrt{2}-2\sqrt{3}+6\sqrt{2}}{3}$$

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

$$\frac{7\sqrt{3}}{3}$$