Find the area of a rectangular object which has a length of 2√3 and a width of 3√6. Explain, in complete sentences, how you arrived at the simplified answer and give the final solution in simplified radical form. What type of object might this be?

Question

Find the area of a rectangular object which has a length of 2√3 and a width of  3√6. Explain, in complete sentences, how you arrived at the simplified answer and give the final solution in simplified radical form. What type of object might this be?

harsimran_hs4 · Answer

what is the area of a rectangular object ?

anonymous · Answer

b x h

harsimran_hs4 · Answer

l * b (l = length b = breadth)
so putting the values given in the ques. what expression do you get ?

anonymous · Answer

2√3 x 3√6 ?

harsimran_hs4 · Answer

yes, so
$$3\sqrt{6} = 3 \sqrt{2\times3} = 3 \sqrt{2}\sqrt{3}$$

harsimran_hs4 · Answer

so 2sqrt(3) * 3sqrt(2)*sqrt(3) = 2*3*(sqrt(3) * sqrt(3))*sqrt(2)

harsimran_hs4 · Answer

clear?

anonymous · Answer

what do you do with the 2√3 ?

harsimran_hs4 · Answer

2sqrt(3) = 2* sqrt(3)

so all i have done is paired this sqrt(3) with other one

anonymous · Answer

are the * = multiplication ?

harsimran_hs4 · Answer

yes

harsimran_hs4 · Answer

generally
+/ - = addition/subtration
* = multiplication
/ = divide
^ = raised to power

anonymous · Answer

ooh so 2√3 x 3√2 x √3 = 2 x 3 x √3 x √3 x √2  is the answer ?

harsimran_hs4 · Answer

no we can simplify more 
sqrt(3) * sqrt(3) = 3
and 2*3 = 6
so 6 * 3 * sqrt(2)
18*sqrt(2)
$$18\sqrt{2}$$ is the answer

anonymous · Answer

okay thank you !