45+12*5/69sqrt{54} eching

$$45+12 \times \frac{ 5 }{ 69 \sqrt{ 54 } }$$

Baholash

$$\frac{10\sqrt{6}}{207}+45\approx 45,118332838$$

Qisqa yechim qadamlari

Faktor: 54=3^{2}\times 6. \sqrt{3^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$45+12\times \frac{5}{69\times 3\sqrt{6}}$$

207 hosil qilish uchun 69 va 3 ni ko'paytirish.

$$45+12\times \frac{5}{207\sqrt{6}}$$

\frac{5}{207\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$45+12\times \frac{5\sqrt{6}}{207\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$45+12\times \frac{5\sqrt{6}}{207\times 6}$$

1242 hosil qilish uchun 207 va 6 ni ko'paytirish.

$$45+12\times \frac{5\sqrt{6}}{1242}$$

12\times \frac{5\sqrt{6}}{1242} ni yagona kasrga aylantiring.

$$45+\frac{12\times 5\sqrt{6}}{1242}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 45 ni \frac{1242}{1242} marotabaga ko'paytirish.

$$\frac{45\times 1242}{1242}+\frac{12\times 5\sqrt{6}}{1242}$$

\frac{45\times 1242}{1242} va \frac{12\times 5\sqrt{6}}{1242} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{45\times 1242+12\times 5\sqrt{6}}{1242}$$

45\times 1242+12\times 5\sqrt{6} ichidagi ko‘paytirishlarni bajaring.

$$\frac{55890+60\sqrt{6}}{1242}$$

Omil

$$\frac{5 {(2 \sqrt{6} + 1863)}}{207} = 45,118332837815615$$