{left(7+6sqrt{88}right)}^2 eching

$${ \left(7+6 \sqrt{ 88 } \right) }^{ 2 }$$

Baholash

$$168\sqrt{22}+3217\approx 4004,98984765$$

Yechim qadamlari

Faktor: 88=2^{2}\times 22. \sqrt{2^{2}\times 22} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{22} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\left(7+6\times 2\sqrt{22}\right)^{2}$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$\left(7+12\sqrt{22}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(7+12\sqrt{22}\right)^{2} kengaytirilishi uchun ishlating.

$$49+168\sqrt{22}+144\left(\sqrt{22}\right)^{2}$$

\sqrt{22} kvadrati – 22.

$$49+168\sqrt{22}+144\times 22$$

3168 hosil qilish uchun 144 va 22 ni ko'paytirish.

$$49+168\sqrt{22}+3168$$

3217 olish uchun 49 va 3168'ni qo'shing.

$$3217+168\sqrt{22}$$

Kengaytirish

$$168 \sqrt{22} + 3217 = 4004,98984765$$

Yechim qadamlari

Faktor: 88=2^{2}\times 22. \sqrt{2^{2}\times 22} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{22} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\left(7+6\times 2\sqrt{22}\right)^{2}$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$\left(7+12\sqrt{22}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(7+12\sqrt{22}\right)^{2} kengaytirilishi uchun ishlating.

$$49+168\sqrt{22}+144\left(\sqrt{22}\right)^{2}$$

\sqrt{22} kvadrati – 22.

$$49+168\sqrt{22}+144\times 22$$

3168 hosil qilish uchun 144 va 22 ni ko'paytirish.

$$49+168\sqrt{22}+3168$$

3217 olish uchun 49 va 3168'ni qo'shing.

$$3217+168\sqrt{22}$$