Divide 4√10 / √2. Provide an exact answer.
1. 2√10
2. This expression is already simplified and cannot be divided further
3. 2√5
4. 4√5
wrong yet again!
4√10 / √2 = 4 √5√2/√2 = 4√5
Your answer was 4√10 / 2 = 2√10
Apologies for the mistake. You are correct. The correct answer is 4√5. Thank you for pointing that out.
To divide 4√10 by √2, we can rationalize the denominator by multiplying the numerator and denominator by √2.
Starting with 4√10 / √2:
4√10 / √2 = (4√10 * √2) / (√2 * √2)
= (4 * √10 * √2) / 2
= (4 * √(10 * 2)) / 2
= (4 * √20) / 2
= 4/2 * √20
= 2 * √20.
Since √20 can be simplified further, we can break it down as √(4 * 5):
2 * √20 = 2 * √(4 * 5)
= 2 * (2√5)
= 4√5.
Therefore, the exact answer to 4√10 / √2 is 4√5. Answer option 4 is correct.
To divide 4√10 by √2, we should simplify the expression by rationalizing the denominator. This means getting rid of any square roots in 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 also √2. So, we have:
(4√10 / √2) * (√2 / √2)
Simplifying this, we get:
(4√10 * √2) / (√2 * √2)
This becomes:
(4√20) / 2
Now, we divide the coefficient (4) by the coefficient (2) and simplify the square root term:
4/2 = 2
√20 = √(2*2*5) = 2√5
Therefore, the simplified form of 4√10 / √2 is:
2√5.
So, the correct answer is option 3.