(2sqrt{3}+3sqrt{2})*(-sqrt{6}) eching

$$( 2 \sqrt { 3 } + 3 \sqrt { 2 } ) \times ( - \sqrt { 6 } )$$

Baholash

$$-6\sqrt{2}-6\sqrt{3}\approx -18,87758622$$

Yechim qadamlari

2\sqrt{3}+3\sqrt{2} ga -\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2\sqrt{3}\left(-\sqrt{6}\right)+3\sqrt{2}\left(-\sqrt{6}\right)$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

$$-2\sqrt{3}\sqrt{6}+3\sqrt{2}\left(-1\right)\sqrt{6}$$

Faktor: 6=3\times 2. \sqrt{3\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$-2\sqrt{3}\sqrt{3}\sqrt{2}+3\sqrt{2}\left(-1\right)\sqrt{6}$$

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

$$-2\times 3\sqrt{2}+3\sqrt{2}\left(-1\right)\sqrt{6}$$

Faktor: 6=2\times 3. \sqrt{2\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$-2\times 3\sqrt{2}+3\sqrt{2}\left(-1\right)\sqrt{2}\sqrt{3}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$-2\times 3\sqrt{2}+3\times 2\left(-1\right)\sqrt{3}$$

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

$$-2\times 3\sqrt{2}+6\left(-1\right)\sqrt{3}$$

-6 hosil qilish uchun 6 va -1 ni ko'paytirish.

$$-2\times 3\sqrt{2}-6\sqrt{3}$$

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

$$-6\sqrt{2}-6\sqrt{3}$$

Omil

$$6 {(-\sqrt{2} - \sqrt{3})} = -18,87758622$$