Divide 2√65 divided by √5. Provide an exact answer. (1 point)
To divide 2√65 by √5, we can simplify the expression as follows:
2√65 / √5
To simplify the expression, we can multiply the numerator and the denominator by √5:
(2√65 / √5) * (√5 / √5)
= (2√65 * √5) / (√5 * √5)
= 2√(65 * 5) / √(5 * 5)
= 2√(325) / √(25)
= 2√(325) / 5
Therefore, the exact answer is 2√(325) / 5.
To divide 2√65 by √5, we can simplify the expression by rationalizing the denominator.
Here's how you can do it step by step:
Step 1: Simplify the expression √65. We can break it down as follows:
√65 = √(5 × 13) = √5 × √13.
Step 2: Substitute the simplified version of √65 back into the original expression:
2√65 = 2 × (√5 × √13).
Step 3: Divide the expression obtained in step 2 by √5:
(2 × √5 × √13) / √5.
Step 4: Rationalize the denominator by multiplying the numerator and denominator by √5:
(2 × √5 × √13 × √5) / (√5 × √5).
Step 5: Simplify the expression in the numerator:
2 × √5 × √13 × √5 = 2 × 5 × √13 = 10√13.
Step 6: Simplify the expression in the denominator:
√5 × √5 = 5.
Step 7: The final expression is 10√13 / 5.
Therefore, the exact answer is 2√13.
To divide 2√65 by √5, we can simplify the expression as follows:
First, we simplify the numerator and denominator individually:
Numerator: 2√65 = 2 * √(5*13) = 2√5√13
Denominator: √5
Next, we divide the numerator by the denominator:
(2√5√13) / √5
Since the denominator is √5 and the numerator has a factor of √5, we can cancel them out:
= 2√13
Therefore, 2√65 divided by √5 is equal to 2√13.