what is the following product?\n$sqrt{30}cdotsqrt{10}$\n$2sqrt{10}$\n$3sqrt{10}$\n$4sqrt{10}$\n$10sqrt{3}$
what is the following product?\n$sqrt{30}cdotsqrt{10}$\n$2sqrt{10}$\n$3sqrt{10}$\n$4sqrt{10}$\n$10sqrt{3}$
Answer
Explanation:
Step1: Use square - root multiplication rule
$\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$ So, $\sqrt{30}\cdot\sqrt{10}=\sqrt{30\times10}=\sqrt{300}$
Step2: Simplify the square - root
$\sqrt{300}=\sqrt{100\times3}$ Since $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 100$, $b = 3$), we have $\sqrt{100\times3}=\sqrt{100}\cdot\sqrt{3}=10\sqrt{3}$
Answer:
$10\sqrt{3}$