sqrt{18^2+(144/sqrt{3})^2}= eching

$$\sqrt { 18 ^ { 2 } + ( \frac { 144 } { \sqrt { 3 } } ) ^ { 2 } } =$$

Baholash

$$6\sqrt{201}\approx 85,064681273$$

Yechim qadamlari

2 daraja ko‘rsatkichini 18 ga hisoblang va 324 ni qiymatni oling.

$$\sqrt{324+\left(\frac{144}{\sqrt{3}}\right)^{2}}$$

\frac{144}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\sqrt{324+\left(\frac{144\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\sqrt{324+\left(\frac{144\sqrt{3}}{3}\right)^{2}}$$

48\sqrt{3} ni olish uchun 144\sqrt{3} ni 3 ga bo‘ling.

$$\sqrt{324+\left(48\sqrt{3}\right)^{2}}$$

\left(48\sqrt{3}\right)^{2} ni kengaytirish.

$$\sqrt{324+48^{2}\left(\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini 48 ga hisoblang va 2304 ni qiymatni oling.

$$\sqrt{324+2304\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\sqrt{324+2304\times 3}$$

6912 hosil qilish uchun 2304 va 3 ni ko'paytirish.

$$\sqrt{324+6912}$$

7236 olish uchun 324 va 6912'ni qo'shing.

$$\sqrt{7236}$$

Faktor: 7236=6^{2}\times 201. \sqrt{6^{2}\times 201} koʻpaytmasining kvadrat ildizini \sqrt{6^{2}}\sqrt{201} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 6^{2} ning kvadrat ildizini chiqarish.

$$6\sqrt{201}$$