Question

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Which of the following is true about the expression sqrt3*sqrt12?
A.It represents the product of two irrational numbers and is equivalent to a rational number.
B.It represents the product of two irrational numbers and is equivalent to an irrational number.
C.It represents the product of two rational numbers and is equivalent to a rational number.
D.It represents the product of two rational numbers and is equivalent to an irrational number.

Answer 1

A. is correct

Explanation:

sqrt3*sqrt12 can be rewritten as √3·√12, which can be extended to

√3·√3·√4.

Note that √4 = 2 and that (√3)^2 = 3,

so the final result is 2*3, or 6 (a rational number).

A. is correct: √3 and √12 are both irrational, but their product is rational.