Question

2 find the product of each radical expression. check your answers graphically. 1. $sqrt{6}cdotsqrt{6}$ 2. $3sqrt{12}cdotsqrt{6}$ 3. $-3sqrt{3}(2 + sqrt{6})$ 4. $-3sqrt{7x^{3}}cdot6sqrt{7x^{3}}$ 5. $sqrt{15x^{2}}cdotsqrt{10x^{3}}$ 6. $sqrt{20x^{2}}cdotsqrt{20x}$ drag & drop the answer $18sqrt{2}$ $5x^{2}sqrt{6x}$ 6 $- 126x^{2}sqrt{x}$ $20xsqrt{x}$ $-6sqrt{3}-9sqrt{2}$ note: use ctrl + d to drag the option via keyboard

Explanation:

Step1: Aplicar la regla $\sqrt{a}\cdot\sqrt{a}=a$

Para $\sqrt{6}\cdot\sqrt{6}$, tenemos $6$.

Step2: Simplificar $\sqrt{12}$ y luego multiplicar

$\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$. Entonces $3\sqrt{12}\cdot\sqrt{6}=3\times2\sqrt{3}\cdot\sqrt{6}=6\sqrt{18}=6\sqrt{9\times2}=18\sqrt{2}$.

Step3: Distribuir el factor exterior

$-3\sqrt{3}(2 + \sqrt{6})=-3\sqrt{3}\times2-3\sqrt{3}\times\sqrt{6}=-6\sqrt{3}-3\sqrt{18}=-6\sqrt{3}-9\sqrt{2}$.

Step4: Multiplicar coeficientes y radicales

$-3\sqrt{7x^{3}}\cdot6\sqrt{7x^{3}}=(-3\times6)\sqrt{7x^{3}\times7x^{3}}=-18\times7x^{3}=-126x^{3}$.

Step5: Multiplicar los radicales y simplificar

$\sqrt{15x^{2}}\cdot\sqrt{10x^{3}}=\sqrt{15x^{2}\times10x^{3}}=\sqrt{150x^{5}}=\sqrt{25\times6x^{4}\times x}=5x^{2}\sqrt{6x}$.

Step6: Multiplicar los radicales y simplificar

$\sqrt{20x^{2}}\cdot\sqrt{20x}=\sqrt{20x^{2}\times20x}=\sqrt{400x^{3}} = 20x\sqrt{x}$.

Answer:

1. $6$
2. $18\sqrt{2}$
3. $-6\sqrt{3}-9\sqrt{2}$
4. $-126x^{3}$
5. $5x^{2}\sqrt{6x}$
6. $20x\sqrt{x}$