Question

multiply. write your answer in simplest form.\\(\sqrt{2} \cdot \sqrt{147}\\)

Explanation:

Step1: Use property of square roots ($\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$)

$\sqrt{2} \cdot \sqrt{147} = \sqrt{2 \times 147}$

Step2: Calculate the product inside the square root

$2 \times 147 = 294$, so we have $\sqrt{294}$

Step3: Factor 294 to simplify the square root

Factor 294: $294 = 49 \times 6$ (since $49 \times 6 = 294$ and 49 is a perfect square)

Step4: Use property $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ again

$\sqrt{49 \times 6} = \sqrt{49} \cdot \sqrt{6}$

Step5: Simplify $\sqrt{49}$

$\sqrt{49} = 7$, so we get $7\sqrt{6}$

Answer:

$7\sqrt{6}$