Which of the following is true about the expression √3-√12?
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.
solve step my step
To determine the nature of the expression √3-√12, we first need to simplify it.
Step 1: Simplify the square roots.
√3 can't be simplified further since 3 is a prime number.
For √12, we can break it down into factors: √(4*3) = √4 * √3 = 2 * √3 = 2√3.
Step 2: Combine like terms.
√3 - 2√3 = -√3.
Now that we have simplified the expression, we can determine its nature.
Observation: The expression contains the square root of 3, which is an irrational number.
To identify the nature of the expression, we need to consider whether the coefficients of the irrational terms are rational or irrational.
In this case, the coefficient of -√3 is -1, which is a rational number.
The product of an irrational number and a rational number is always an irrational number.
Therefore, the correct answer is D) It represents the product of two rational numbers and is equivalent to an irrational number.