Divide (4sqrt(10))/(sqrt(2)) Provide an exact answer. (1 point)
2sqrt(5)
2sqrt(10)
This expression is already simplified and cannot be divided further.
O 4sqrt(5)
The exact answer is 2sqrt(5).
To divide (4√10) by √2, we rationalize the denominator by multiplying both the numerator and denominator by √2.
(4√10)/(√2) = (4√10 * √2) / (√2 * √2)
Simplifying, we get:
(4√20)/(√4)
Since √20 = √(4*5) = 2√5, and √4 = 2, we can substitute these values into the expression:
(4 * 2√5) / 2
Simplifying further:
(8√5) / 2
Finally, we divide 8 by 2 to get the final answer:
4√5
To divide (4sqrt(10)) by (sqrt(2)), we can use the rules of dividing square roots.
Step 1: Simplify the denominator.
Since sqrt(2) cannot be simplified further, we leave it as is.
Step 2: Simplify the numerator.
To simplify 4sqrt(10), we can break it down into two parts: the coefficient 4 and the square root term sqrt(10).
Step 3: Divide the numerator by the denominator.
Dividing the numerator (4sqrt(10)) by the denominator (sqrt(2)) is equivalent to multiplying the numerator by the conjugate of the denominator (which is sqrt(2)). This will eliminate the square root term in the denominator.
(4sqrt(10))/(sqrt(2)) = (4sqrt(10))(sqrt(2))/(sqrt(2))(sqrt(2))
In the numerator, sqrt(2) multiplied by sqrt(2) equals 2.
(4sqrt(10))(sqrt(2))/(2)
= (4*2*sqrt(10))/(2)
= 8sqrt(10)/2
= 4sqrt(10)
So, the exact answer is 4sqrt(10).