Question

16 when expanded and simplified as a mixed radical, the value of $sqrt{3}left(sqrt{12}+sqrt{15}
ight)$ is
a. $sqrt{15}+3sqrt{2}$
b. $6 + 3sqrt{5}$
c. $6+sqrt{15}$
d. $sqrt{81}$

Explanation:

Step1: Simplify $\sqrt{12}$

$\sqrt{12} = \sqrt{4\times3} = 2\sqrt{3}$

Step2: Substitute back to the expression

$\sqrt{3} \times (2\sqrt{3} + \sqrt{15})$

Step3: Distribute $\sqrt{3}$

$\sqrt{3} \times 2\sqrt{3} + \sqrt{3} \times \sqrt{15}$

Step4: Calculate each term

First term: $\sqrt{3} \times 2\sqrt{3} = 2\times(\sqrt{3})^2 = 2\times3 = 6$
Second term: $\sqrt{3} \times \sqrt{15} = \sqrt{3\times15} = \sqrt{45} = \sqrt{9\times5} = 3\sqrt{5}$

Step5: Combine the terms

$6 + 3\sqrt{5}$

Answer:

B. $6+3\sqrt{5}$