$$ \sqrt {3} imes (\sqrt {3}-\sqrt {27)}-(3-\sqrt {3})^{2} $$

Question

$$ \sqrt {3}	imes (\sqrt {3}-\sqrt {27)}-(3-\sqrt {3})^{2} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{3}\times \left(\sqrt{3}-\sqrt{27}\right)-\left(3-\sqrt{3}\right)^{2}$$
- step1: Simplify the root:
  $$\sqrt{3}\times \left(\sqrt{3}-3\sqrt{3}\right)-\left(3-\sqrt{3}\right)^{2}$$
- step2: Subtract the numbers:
  $$\sqrt{3}\times \left(-2\sqrt{3}\right)-\left(3-\sqrt{3}\right)^{2}$$
- step3: Multiply the numbers:
  $$-6-\left(3-\sqrt{3}\right)^{2}$$
- step4: Evaluate the power:
  $$-6-12+6\sqrt{3}$$
- step5: Subtract the numbers:
  $$-18+6\sqrt{3}$$
Para resolver la expresión $$ \sqrt{3} \times (\sqrt{3} - \sqrt{27}) - (3 - \sqrt{3})^{2} $$, seguimos estos pasos:

1. **Calcular $$ \sqrt{27} $$**:
   $$
   \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}
   $$

2. **Sustituir $$ \sqrt{27} $$ en la expresión**:
   $$
   \sqrt{3} \times (\sqrt{3} - 3\sqrt{3}) = \sqrt{3} \times (-2\sqrt{3}) = -2 \times 3 = -6
   $$

3. **Calcular $$ (3 - \sqrt{3})^{2} $$**:
   $$
   (3 - \sqrt{3})^{2} = 3^{2} - 2 \times 3 \times \sqrt{3} + (\sqrt{3})^{2} = 9 - 6\sqrt{3} + 3 = 12 - 6\sqrt{3}
   $$

4. **Sustituir en la expresión original**:
   $$
   -6 - (12 - 6\sqrt{3}) = -6 - 12 + 6\sqrt{3} = -18 + 6\sqrt{3}
   $$

Por lo tanto, el resultado simplificado de la expresión es:
$$
-18 + 6\sqrt{3}
$$
El resultado simplificado de la expresión es $$ -18 + 6\sqrt{3} $$.

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