simplify.\n10\\sqrt{45}

Explanation:

Step1: Factorize 45

$45 = 9\times5$

Step2: Rewrite the square - root

$10\sqrt{45}=10\sqrt{9\times5}$

Step3: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 9$, $b = 5$)

$10\sqrt{9\times5}=10\times\sqrt{9}\times\sqrt{5}$

Step4: Evaluate $\sqrt{9}$

Since $\sqrt{9}=3$, then $10\times\sqrt{9}\times\sqrt{5}=10\times3\times\sqrt{5}$

Step5: Calculate the product

$10\times3\times\sqrt{5}=30\sqrt{5}$

Answer:

$30\sqrt{5}$