Divide 410√2√. Provide an exact answer. (1 point)
Responses
210−−√
2 start root 10 end root
45–√
4 start root 5 end root
This expression is already simplified and cannot be divided further.
This expression is already simplified and cannot be divided further.
25–√
5 start root 2 end root
To divide 410√2√, we can first simplify the expression by multiplying the square roots together:
410√2√ = 410√(2 * √2) = 410√(2 * 2) = 410√4
Since the square root of 4 is 2, we can further simplify the expression:
410√4 = 410 * 2 = 820
Therefore, the exact answer is 820.
To divide 410√2 by √5, we need to simplify the expression first.
First, let's simplify √5. The square root of 5 cannot be simplified further, so it remains as it is: √5.
Now, let's simplify 410√2. We can break it down into two parts: 410 and √2.
Next, let's simplify 410. It is not divisible by 5, so we can keep it as it is: 410.
Finally, let's simplify √2. The square root of 2 cannot be simplified further, so it remains as it is: √2.
Putting it all together, we have 410√2/ √5.
To divide these expressions, we need to rationalize the denominator. To do this, we multiply the numerator and denominator by √5 to eliminate the radical in the denominator.
(410√2 * √5) / (√5 * √5)
Expanding both the numerator and the denominator, we get:
(410√10) / 5
Therefore, the exact answer is 82√10.