Divide 4√10/√2 . Provide an exact answer. (1 point)
Responses
4√5
4 start root 5 end root
2√10
2 start root 10 end root
This expression is already simplified and cannot be divided further.
This expression is already simplified and cannot be divided further.
2√5
2 start root 5 end root
The correct answer is 2√5.
To divide 4√10/√2, we can simplify by rationalizing the denominator.
First, let's rationalize the denominator:
√2 * √2 = 2
Now, we can divide the numerator by the denominator:
4√10/√2 = (4√10 * √2)/2
Next, let's simplify the numerator:
4√10 * √2 = 4√(10*2) = 4√20 = 4 * √4 * √5 = 8√5
Now, we can substitute the simplified numerator into the division equation:
(8√5)/2 = 4√5
Therefore, the exact answer to the division 4√10/√2 is 4√5.
To divide 4√10/√2, we need to rationalize the denominator (get rid of the square root in the denominator).
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √2 is √2 itself.
So, we have:
(4√10/√2) * (√2/√2)
Multiplying numerator and denominator gives us:
(4√10 * √2) / (√2 * √2)
= (4√10 * √2) / 2
= (4 * √10 * √2) / 2
= (4 * √10√2) / 2
Simplifying further:
= (4 * √(10 * 2)) / 2
= (4 * √20) / 2
Since 20 can be simplified to 4 * 5, we have:
= (4 * √(4 * 5)) / 2
= (4 * √4 * √5) / 2
= (4 * 2 * √5) / 2
= (8 * √5) / 2
Finally, dividing:
= 8√5 / 2
= 4√5
So, the exact answer is 4√5.