divide 2√65 / √5 . provide an exact answer.
the answer 2√325 / 5 is incorrect, so is 2/5√325
divide, not multiply. this is radicals.
To simplify the expression (2√65) / √5, we can follow these steps:
Step 1: Rationalize the Denominator
Since the denominator contains a square root, we need to rationalize it by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √5 is (-√5).
(2√65 / √5) * (-√5 / -√5)
= (-2√325 / 5)
Step 2: Simplify the Root Term
Now let's simplify the root term. Since 325 is not a perfect square, we need to break it down into its factors.
325 = 13 * 25
Now we can simplify the expression further:
(-2√325 / 5) = (-2 * √(13 * 25) / 5)
= (-2 * 5√13 / 5)
= -2√13
Therefore, the simplified expression (2√65) / √5 is equal to -2√13.
To divide 2√65 by √5, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of √5, which is also √5.
Here's how it is done:
(2√65 / √5) * (√5 / √5)
Simplifying further:
(2√65 * √5) / (√5 * √5)
= 2√(65*5) / √(5*5)
= 2√(325) / √(25)
= 2√(325) / 5
Therefore, the exact answer is 2√(325) / 5 or (2/5)√325.
Apologies for the incorrect response. Let's calculate the division properly:
We have 2√65 / √5.
To simplify this expression, we can multiply the numerator and denominator by √5:
(2√65 / √5) * (√5 / √5)
This gives us:
= (2√65 * √5) / (√5 * √5)
= (2√(65*5)) / 5
= (2√(325)) / 5
Thus, the exact answer is (2√325) / 5.
Apologies for the mistake. Let's divide 2√65 by √5 correctly:
We have (2√65) / √5.
To divide these radicals, we can rationalize the denominator by multiplying both the numerator and denominator by √5:
[(2√65) / √5] * [√5 / √5]
Simplifying further:
= (2√(65*5)) / (5)
= (2√(325)) / 5
Thus, the exact answer is (2√325) / 5.