Question

Which choice is equivalent to the product below?


`\sqrt{(3)/(16)} *\sqrt{(3)/(9)}`

a. 1/2
b. 6/12
c. 3/4
d. 3/12
e. 7/12

Answer 1

`\bf \sqrt{\cfrac{3}{16}}\cdot \sqrt{\cfrac{3}{9}}\implies \cfrac{√(3)}{√(16)}\cdot \cfrac{√(3)}{√(9)}\implies \cfrac{√(3)}{4}\cdot \cfrac{√(3)}{3}\implies \cfrac{√(3)\cdot √(3)}{4\cdot 3} \\\\\\ \cfrac{(√(3))^2}{12}\implies \boxed{\cfrac{3}{12}}\implies \stackrel{simplified}{\cfrac{1}{4}}`