Question

Simplify 2 square root of 10 times 3 square root of 12
answers
A.6squar rootof120

B.12squar rootof60

C.12squar rootof30

D.5squar rootof120

Answer 1

We are asked to simplify $2 \sqrt{10} * 3 \sqrt{12}$.

i) using the property :

$\sqrt{a} * \sqrt{b} = \sqrt{ab}$

we write $2 \sqrt{10} * 3 \sqrt{12}$

as $2*3* \sqrt{10} *\sqrt{12}=6 \sqrt{120}$

ii) we factorize 120 to see whether there are perfect squares, to take out of the square root.

$120=12*10=3*4*2*5= 2^{2} *3*2*5=2^{2}*30$

thus, 

$6 \sqrt{120}=6 \sqrt{2^{2}*30} =6* \sqrt{ 2^{2} } * \sqrt{30} =6*2* \sqrt{30}=12 \sqrt{30}$


Answer: C)  $12 \sqrt{30}$