Divide 4√10/√2. Provide an exact answer.
a. 4√5
b. 2√5
c. 2√10
d. This expression is already simplified and cannot be divided
To divide 4√10/√2, we can rationalize the denominator by multiplying both the numerator and denominator by √2:
(4√10/√2) * (√2/√2) = (4√10 * √2) / (√2 * √2) = (4√20) / √4
Next, we can simplify the expression:
(4√20) / √4 = (4√20) / 2 = 2√20 = 2(√4 * √5) = 2(2√5) = 4√5
Therefore, the exact answer is a. 4√5.
To divide the expression 4√10/√2, we need to apply the rules of dividing radicals. We can simplify this expression by rationalizing the denominator.
Step 1: Rationalize the denominator
√2 can be rationalized by multiplying both the numerator and denominator by the conjugate of √2, which is also √2.
(4√10/√2) * (√2/√2) = (4√20)/(√2√2) = (4√20)/2 = 2√20
Step 2: Simplify the expression
√20 can be further simplified by breaking it down into its prime factors.
√20 = √(4 * 5) = √4 * √5 = 2√5
So, the simplified expression is 2√5.
Therefore, the correct answer is b. 2√5.