sqrt{27}-2*(1+sqrt{9}+2*sqrt{27}+sqrt{36}-2*sqrt{3}-sqrt{4}-sqrt{64}) eching

$$\sqrt { 27 } - 2 \cdot ( 1 + \sqrt { 9 } + 2 \cdot \sqrt { 27 } + \sqrt { 36 } - 2 \cdot \sqrt { 3 } - \sqrt { 4 } - \sqrt { 64 } )$$

Baholash

$$-5\sqrt{3}\approx -8,660254038$$

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.

$$3\sqrt{3}-2\left(1+\sqrt{9}+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(1+3+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(4+2\sqrt{27}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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.

$$3\sqrt{3}-2\left(4+2\times 3\sqrt{3}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(4+6\sqrt{3}+\sqrt{36}-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(4+6\sqrt{3}+6-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(10+6\sqrt{3}-2\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(10+4\sqrt{3}-\sqrt{4}-\sqrt{64}\right)$$

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

$$3\sqrt{3}-2\left(10+4\sqrt{3}-2-\sqrt{64}\right)$$

8 olish uchun 10 dan 2 ni ayirish.

$$3\sqrt{3}-2\left(8+4\sqrt{3}-\sqrt{64}\right)$$

64 ning kvadrat ildizini hisoblab, 8 natijaga ega bo‘ling.

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

0 olish uchun 8 dan 8 ni ayirish.

$$3\sqrt{3}-2\times 4\sqrt{3}$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$3\sqrt{3}-8\sqrt{3}$$

-5\sqrt{3} ni olish uchun 3\sqrt{3} va -8\sqrt{3} ni birlashtirish.

$$-5\sqrt{3}$$