Divide 4√10 / √2. Provide an exact answer. (1 point)
To divide the expression 4√10 by √2, we can simplify the denominator first.
√2 can be written as √(2*1), or √2.
Now, we can rewrite the expression as:
4√(10) / √(2)
To divide, we can multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √2 is -√2.
(4√(10) / √(2)) * (-√2 / -√2)
This simplifies to:
(-4√(20) / 2)
We can further simplify the expression by factoring out the square root term:
(-4 * √(4*5) / 2)
This becomes:
(-4 * 2√5 / 2)
The 2's cancel out, leaving:
-4√5
Therefore, the exact answer to 4√10 / √2 is -4√5.
To divide the expression 4√10 by √2, we need to rationalize the denominator.
Step 1: Multiply the numerator and denominator by the conjugate of the denominator, which is also √2.
(4√10 / √2) * (√2 / √2) = (4√20) / 2
Step 2: Simplify the expression inside the square root.
4√20 = 4√(4 * 5) = 4√4 * √5 = 4 * 2 * √5 = 8√5
Step 3: Simplify the expression.
(8√5) / 2 = 4√5
Therefore, the exact answer is 4√5.
its 4√5. correct?
Apologies for the mistake in my previous response. You are correct. The exact answer is 4√5.
To divide 4√10 by √2, we need to rationalize the denominator.
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator.
The conjugate of √2 is √2 itself (since the conjugate of a square root is the same square root with the sign switched).
So, we multiply both the numerator and the denominator by √2:
(4√10 / √2) * (√2 / √2)
Simplifying this expression, we have:
(4√10 * √2) / (√2 * √2)
Multiplying the numerators and denominators separately, we get:
(4√20) / (√2 * √2)
Simplifying the denominator:
(4√20) / √(2^2)
This becomes:
(4√20) / √4
Simplifying further, we have:
(4 * √(10 * 2)) / (√(2^2))
Combining the square roots:
(4 * √(20)) / (√4)
Simplifying the square roots:
(4 * 2√5) / 2
Canceling out the common factor of 2:
4√5
Therefore, the exact answer is 4√5.