sqrt{{left(5/4right)}^2+{left(5/2right)}^2-5} eching

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

Baholash

$$\frac{3\sqrt{5}}{4}\approx 1,677050983$$

Yechim qadamlari

2 daraja ko‘rsatkichini \frac{5}{4} ga hisoblang va \frac{25}{16} ni qiymatni oling.

$$\sqrt{\frac{25}{16}+\left(\frac{5}{2}\right)^{2}-5}$$

2 daraja ko‘rsatkichini \frac{5}{2} ga hisoblang va \frac{25}{4} ni qiymatni oling.

$$\sqrt{\frac{25}{16}+\frac{25}{4}-5}$$

16 va 4 ning eng kichik umumiy karralisi 16 ga teng. \frac{25}{16} va \frac{25}{4} ni 16 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{25}{16}+\frac{100}{16}-5}$$

\frac{25}{16} va \frac{100}{16} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{25+100}{16}-5}$$

125 olish uchun 25 va 100'ni qo'shing.

$$\sqrt{\frac{125}{16}-5}$$

5 ni \frac{80}{16} kasrga o‘giring.

$$\sqrt{\frac{125}{16}-\frac{80}{16}}$$

\frac{125}{16} va \frac{80}{16} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{125-80}{16}}$$

45 olish uchun 125 dan 80 ni ayirish.

$$\sqrt{\frac{45}{16}}$$

\sqrt{\frac{45}{16}} boʻlinmasining kvadrat ildizini \frac{\sqrt{45}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{45}}{\sqrt{16}}$$

Faktor: 45=3^{2}\times 5. \sqrt{3^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{3\sqrt{5}}{\sqrt{16}}$$

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

$$\frac{3\sqrt{5}}{4}$$