Divide 2√65 provide an exact answer
√5
To divide 2√65, we can simplify it by dividing the coefficients and dividing the radicands separately.
First, let's divide the coefficients: 2 ÷ 1 = 2.
Next, let's divide the radicands: √65 ÷ √5.
To divide the radicands, we can simplify them by finding perfect square factors. We notice that 65 can be factored as 13 * 5, and 5 is a perfect square. Thus, we can rewrite 65 as √(13 * 5) = √13 * √5.
Now, the expression becomes 2(√13 * √5) ÷ √5.
Since we have a common radicand of √5 in both the numerator and denominator, we can cancel it out, which leaves us with:
2√13.
Therefore, dividing 2√65 provides an exact answer of 2√13.
To divide 2√65, we can simplify the expression as follows:
2√65 ÷ √5
Since the denominator (√5) is a square root, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of √5, which is also √5:
(2√65 ÷ √5) * (√5/√5)
Simplifying this expression:
= (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, we can rationalize the denominator.
Step 1: Simplify the radicand (number inside the square root):
√65 = √(5 * 13) = √5 * √13
Step 2: Rewrite the expression with the simplified radicand:
2√65 = 2(√5 * √13)
Step 3: Distribute the 2 to both terms inside the parentheses:
2(√5 * √13) = 2√5 * 2√13
Step 4: Multiply the coefficients and the square roots separately:
2√5 * 2√13 = (2 * 2) * (√5 * √13) = 4√65
Therefore, 2√65 divided by √5 is equal to 4√65.