Divide 410√ / 2√ . Provide an exact answer. (1 point)
Responses
210−−√
2 start root 10 end root
45–√
4 start root 5 end root
25–√
2 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.
This expression is already simplified and cannot be divided further.
To divide 410√ by 2√, we can simplify the expression by rationalizing the denominator. Rationalizing the denominator involves eliminating the square root in the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
In this case, the conjugate of 2√ is also 2√.
So, we multiply the numerator and denominator by 2√:
(410√ * 2√) / (2√ * 2√)
Simplifying the expression:
820 / 2
The answer is 410.
To divide the expression 410√ / 2√, we can simplify it by canceling out the common factors inside the square roots.
First, we can simplify the expression by dividing the numbers outside the square roots:
410 / 2 = 205
Next, we divide the square roots by canceling out the common factors. Both 410 and 2 have a factor of √10:
√(410/2) / √(2/2) = √205 / √1
Since the square root of 1 is equal to 1, we can simplify further:
√205 / 1 = √205
Therefore, the exact answer to the expression 410√ / 2√ is √205.