711+196*34/sqrt{46224} eching

$$711 + 196 \times \frac { 34 } { \sqrt { 46224 } }$$

Baholash

$$\frac{1666\sqrt{321}}{963}+711\approx 741,995684109$$

Qisqa yechim qadamlari

Faktor: 46224=12^{2}\times 321. \sqrt{12^{2}\times 321} koʻpaytmasining kvadrat ildizini \sqrt{12^{2}}\sqrt{321} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 12^{2} ning kvadrat ildizini chiqarish.

$$711+196\times \frac{34}{12\sqrt{321}}$$

\frac{34}{12\sqrt{321}} maxrajini \sqrt{321} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$711+196\times \frac{34\sqrt{321}}{12\left(\sqrt{321}\right)^{2}}$$

\sqrt{321} kvadrati – 321.

$$711+196\times \frac{34\sqrt{321}}{12\times 321}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$711+196\times \frac{17\sqrt{321}}{6\times 321}$$

1926 hosil qilish uchun 6 va 321 ni ko'paytirish.

$$711+196\times \frac{17\sqrt{321}}{1926}$$

196\times \frac{17\sqrt{321}}{1926} ni yagona kasrga aylantiring.

$$711+\frac{196\times 17\sqrt{321}}{1926}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 711 ni \frac{1926}{1926} marotabaga ko'paytirish.

$$\frac{711\times 1926}{1926}+\frac{196\times 17\sqrt{321}}{1926}$$

\frac{711\times 1926}{1926} va \frac{196\times 17\sqrt{321}}{1926} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{711\times 1926+196\times 17\sqrt{321}}{1926}$$

711\times 1926+196\times 17\sqrt{321} ichidagi ko‘paytirishlarni bajaring.

$$\frac{1369386+3332\sqrt{321}}{1926}$$