(sqrt{3}+sqrt{15})^2 eching

$$( \sqrt { 3 } + \sqrt { 15 } ) ^ { 2 }$$

Baholash

$$6\left(\sqrt{5}+3\right)\approx 31,416407865$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\sqrt{3}+\sqrt{15}\right)^{2} kengaytirilishi uchun ishlating.

$$\left(\sqrt{3}\right)^{2}+2\sqrt{3}\sqrt{15}+\left(\sqrt{15}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$3+2\sqrt{3}\sqrt{15}+\left(\sqrt{15}\right)^{2}$$

Faktor: 15=3\times 5. \sqrt{3\times 5} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$3+2\sqrt{3}\sqrt{3}\sqrt{5}+\left(\sqrt{15}\right)^{2}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$3+2\times 3\sqrt{5}+\left(\sqrt{15}\right)^{2}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$3+6\sqrt{5}+\left(\sqrt{15}\right)^{2}$$

\sqrt{15} kvadrati – 15.

$$3+6\sqrt{5}+15$$

18 olish uchun 3 va 15'ni qo'shing.

$$18+6\sqrt{5}$$

Kengaytirish

$$6 \sqrt{5} + 18 = 31,416407865$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\sqrt{3}+\sqrt{15}\right)^{2} kengaytirilishi uchun ishlating.

$$\left(\sqrt{3}\right)^{2}+2\sqrt{3}\sqrt{15}+\left(\sqrt{15}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$3+2\sqrt{3}\sqrt{15}+\left(\sqrt{15}\right)^{2}$$

Faktor: 15=3\times 5. \sqrt{3\times 5} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$3+2\sqrt{3}\sqrt{3}\sqrt{5}+\left(\sqrt{15}\right)^{2}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$3+2\times 3\sqrt{5}+\left(\sqrt{15}\right)^{2}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$3+6\sqrt{5}+\left(\sqrt{15}\right)^{2}$$

\sqrt{15} kvadrati – 15.

$$3+6\sqrt{5}+15$$

18 olish uchun 3 va 15'ni qo'shing.

$$18+6\sqrt{5}$$