sqrt{{left(9/2right)}^2+6^2}+sqrt{{left(9/2right)}^2-129/2+4} eching

$$\sqrt{ { \left( \frac{ 9 }{ 2 } \right) }^{ 2 } + { 6 }^{ 2 } } + \sqrt{ { \left( \frac{ 9 }{ 2 } \right) }^{ 2 } -12 \frac{ 9 }{ 2 } +4 }$$

Baholash

$$\frac{\sqrt{31}+15}{2}\approx 10,283882181$$

Yechim qadamlari

2 daraja ko‘rsatkichini \frac{9}{2} ga hisoblang va \frac{81}{4} ni qiymatni oling.

$$\sqrt{\frac{81}{4}+6^{2}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$\sqrt{\frac{81}{4}+36}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

36 ni \frac{144}{4} kasrga o‘giring.

$$\sqrt{\frac{81}{4}+\frac{144}{4}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

\frac{81}{4} va \frac{144}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{81+144}{4}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

225 olish uchun 81 va 144'ni qo'shing.

$$\sqrt{\frac{225}{4}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

\frac{225}{4} boʻlinmasining kvadrat ildizini \frac{\sqrt{225}}{\sqrt{4}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{15}{2}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

2 daraja ko‘rsatkichini \frac{9}{2} ga hisoblang va \frac{81}{4} ni qiymatni oling.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{12\times 2+9}{2}+4}$$

24 hosil qilish uchun 12 va 2 ni ko'paytirish.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{24+9}{2}+4}$$

33 olish uchun 24 va 9'ni qo'shing.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{33}{2}+4}$$

4 va 2 ning eng kichik umumiy karralisi 4 ga teng. \frac{81}{4} va \frac{33}{2} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{66}{4}+4}$$

\frac{81}{4} va \frac{66}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{15}{2}+\sqrt{\frac{81-66}{4}+4}$$

15 olish uchun 81 dan 66 ni ayirish.

$$\frac{15}{2}+\sqrt{\frac{15}{4}+4}$$

4 ni \frac{16}{4} kasrga o‘giring.

$$\frac{15}{2}+\sqrt{\frac{15}{4}+\frac{16}{4}}$$

\frac{15}{4} va \frac{16}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{15}{2}+\sqrt{\frac{15+16}{4}}$$

31 olish uchun 15 va 16'ni qo'shing.

$$\frac{15}{2}+\sqrt{\frac{31}{4}}$$

\sqrt{\frac{31}{4}} boʻlinmasining kvadrat ildizini \frac{\sqrt{31}}{\sqrt{4}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{15}{2}+\frac{\sqrt{31}}{\sqrt{4}}$$

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

$$\frac{15}{2}+\frac{\sqrt{31}}{2}$$

\frac{15}{2} va \frac{\sqrt{31}}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{15+\sqrt{31}}{2}$$

Omil

$$\frac{\sqrt{31} + 15}{2} = 10,283882181415011$$