sqrt{(6sqrt{6})^2+(6sqrt{2})^2} eching

$$\sqrt { ( 6 \sqrt { 6 } ) ^ { 2 } + ( 6 \sqrt { 2 } ) ^ { 2 } }$$

Baholash

$$12\sqrt{2}\approx 16,970562748$$

Yechim qadamlari

\left(6\sqrt{6}\right)^{2} ni kengaytirish.

$$\sqrt{6^{2}\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

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

$$\sqrt{36\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$\sqrt{36\times 6+\left(6\sqrt{2}\right)^{2}}$$

216 hosil qilish uchun 36 va 6 ni ko'paytirish.

$$\sqrt{216+\left(6\sqrt{2}\right)^{2}}$$

\left(6\sqrt{2}\right)^{2} ni kengaytirish.

$$\sqrt{216+6^{2}\left(\sqrt{2}\right)^{2}}$$

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

$$\sqrt{216+36\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\sqrt{216+36\times 2}$$

72 hosil qilish uchun 36 va 2 ni ko'paytirish.

$$\sqrt{216+72}$$

288 olish uchun 216 va 72'ni qo'shing.

$$\sqrt{288}$$

Faktor: 288=12^{2}\times 2. \sqrt{12^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{12^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 12^{2} ning kvadrat ildizini chiqarish.

$$12\sqrt{2}$$