sqrt{80}+5sqrt{1/2}-3sqrt{+1/5}sqrt{125} eching

$$\sqrt{ 80 } +5 \sqrt{ \frac{ 1 }{ 2 } } -3 \sqrt{ + \frac{ 1 }{ 5 } } \sqrt{ 125 }$$

Baholash

$$\frac{5\sqrt{2}}{2}+4\sqrt{5}-15\approx -2,520194184$$

Qisqa yechim qadamlari

Faktor: 80=4^{2}\times 5. \sqrt{4^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$4\sqrt{5}+5\sqrt{\frac{1}{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{1}{\sqrt{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

\sqrt{2} kvadrati – 2.

$$4\sqrt{5}+5\times \frac{\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+\frac{5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$\frac{2\times 4\sqrt{5}}{2}+\frac{5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

\frac{2\times 4\sqrt{5}}{2} va \frac{5\sqrt{2}}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\times 4\sqrt{5}+5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

2\times 4\sqrt{5}+5\sqrt{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

\sqrt{\frac{1}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{1}}{\sqrt{5}}\sqrt{125}$$

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

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{1}{\sqrt{5}}\sqrt{125}$$

\frac{1}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{125}$$

\sqrt{5} kvadrati – 5.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{5}}{5}\sqrt{125}$$

Faktor: 125=5^{2}\times 5. \sqrt{5^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{5}}{5}\times 5\sqrt{5}$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-15\times \frac{\sqrt{5}}{5}\sqrt{5}$$

15 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\sqrt{5}\sqrt{5}$$

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

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-\frac{2\times 3\sqrt{5}\sqrt{5}}{2}$$

\frac{8\sqrt{5}+5\sqrt{2}}{2} va \frac{2\times 3\sqrt{5}\sqrt{5}}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{8\sqrt{5}+5\sqrt{2}-2\times 3\sqrt{5}\sqrt{5}}{2}$$

8\sqrt{5}+5\sqrt{2}-2\times 3\sqrt{5}\sqrt{5} ichidagi ko‘paytirishlarni bajaring.

$$\frac{8\sqrt{5}+5\sqrt{2}-30}{2}$$