3*sqrt{27}-2*(1+sqrt{9}+2*sqrt{27}+sqrt{36}-2sqrt{3}-sqrt{4}-18) eching

$$3 \cdot \sqrt { 27 } - 2 \cdot ( 1 + \sqrt { 9 } + 2 \cdot \sqrt { 27 } + \sqrt { 36 } - 2 \sqrt { 3 } - \sqrt { 4 } - 18 )$$

Baholash

$$\sqrt{3}+20\approx 21,732050808$$

Yechim qadamlari

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$3\times 3\sqrt{3}-2\left(1+\sqrt{9}+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-18\right)$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$9\sqrt{3}-2\left(1+\sqrt{9}+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-18\right)$$

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

$$9\sqrt{3}-2\left(1+3+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-18\right)$$

4 olish uchun 1 va 3'ni qo'shing.

$$9\sqrt{3}-2\left(4+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-18\right)$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$9\sqrt{3}-2\left(4+2\times 3\sqrt{3}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-18\right)$$

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

$$9\sqrt{3}-2\left(4+6\sqrt{3}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-18\right)$$

36 ning kvadrat ildizini hisoblab, 6 natijaga ega bo‘ling.

$$9\sqrt{3}-2\left(4+6\sqrt{3}+6-2\sqrt{3}-\sqrt{4}-18\right)$$

10 olish uchun 4 va 6'ni qo'shing.

$$9\sqrt{3}-2\left(10+6\sqrt{3}-2\sqrt{3}-\sqrt{4}-18\right)$$

4\sqrt{3} ni olish uchun 6\sqrt{3} va -2\sqrt{3} ni birlashtirish.

$$9\sqrt{3}-2\left(10+4\sqrt{3}-\sqrt{4}-18\right)$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$9\sqrt{3}-2\left(10+4\sqrt{3}-2-18\right)$$

8 olish uchun 10 dan 2 ni ayirish.

$$9\sqrt{3}-2\left(8+4\sqrt{3}-18\right)$$

-10 olish uchun 8 dan 18 ni ayirish.

$$9\sqrt{3}-2\left(-10+4\sqrt{3}\right)$$

-2 ga -10+4\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9\sqrt{3}+20-8\sqrt{3}$$

\sqrt{3} ni olish uchun 9\sqrt{3} va -8\sqrt{3} ni birlashtirish.

$$\sqrt{3}+20$$