(sqrt{32}+sqrt{05}-2sqrt{1/3})-(sqrt{1/8}-sqrt{75}) eching

$$( \sqrt { 32 } + \sqrt { 05 } - 2 \sqrt { \frac { 1 } { 3 } } ) - ( \sqrt { \frac { 1 } { 8 } } - \sqrt { 75 } )$$

Baholash

$$\frac{13\sqrt{3}}{3}+\frac{15\sqrt{2}}{4}\approx 12,808854358$$

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.

$$4\sqrt{2}+\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+\sqrt{0}-2\sqrt{\frac{1}{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0-2\sqrt{\frac{1}{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0-2\times \frac{1}{\sqrt{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

\sqrt{3} kvadrati – 3.

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{3\left(4\sqrt{2}+0\right)}{3}+\frac{-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{3\left(4\sqrt{2}+0\right)-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{1}}{\sqrt{8}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{1}{\sqrt{8}}-\sqrt{75}\right)$$

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.

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{1}{2\sqrt{2}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\sqrt{75}\right)$$

\sqrt{2} kvadrati – 2.

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{2}}{2\times 2}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{2}}{4}-\sqrt{75}\right)$$

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.

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

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

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

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

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

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\frac{\sqrt{2}-20\sqrt{3}}{4}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 4 ning eng kichik umumiy karralisi 12. \frac{12\sqrt{2}-2\sqrt{3}}{3} ni \frac{4}{4} marotabaga ko'paytirish. \frac{\sqrt{2}-20\sqrt{3}}{4} ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{4\left(12\sqrt{2}-2\sqrt{3}\right)}{12}-\frac{3\left(\sqrt{2}-20\sqrt{3}\right)}{12}$$

\frac{4\left(12\sqrt{2}-2\sqrt{3}\right)}{12} va \frac{3\left(\sqrt{2}-20\sqrt{3}\right)}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{4\left(12\sqrt{2}-2\sqrt{3}\right)-3\left(\sqrt{2}-20\sqrt{3}\right)}{12}$$

4\left(12\sqrt{2}-2\sqrt{3}\right)-3\left(\sqrt{2}-20\sqrt{3}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{48\sqrt{2}-8\sqrt{3}-3\sqrt{2}+60\sqrt{3}}{12}$$

48\sqrt{2}-8\sqrt{3}-3\sqrt{2}+60\sqrt{3} hisob-kitobini qiling.

$$\frac{45\sqrt{2}+52\sqrt{3}}{12}$$