Question

2 √65 divided by √5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To divide √65 by √5, you can simplify the expression using the properties of radicals.

First, rewrite √65 as √(13*5) = √13 * √5.
Similarly, rewrite √5 as √(5*1) = √5.

Now, the expression becomes (√13 * √5) / √5.

Since √5/√5 = 1, the expression simplifies to just √13.

Therefore, 2 √65 divided by √5 is equal to 2√13.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression, we can combine the square roots in the numerator and denominator:

√65 = √(5 * 13)
√5 ÷ √5 = 1

Therefore,

2 √65 ÷ √5
= 2 * (√(5 * 13)) ÷ √5
= 2 * (√5 * √13) ÷ √5
= 2 * (√5 / √5) * √13
= 2 * 1 * √13
= 2√13

So, 2 √65 ÷ √5 simplifies to 2√13.

Answer 3

[AI-generated answer — Explain Bot]

To divide 2√65 by √5, we'll follow these steps:

Step 1: Simplify each square root individually.

√65 = √(13 × 5). Since there are no perfect square factors in 65, we can't simplify it further.

√5 = √(5 × 1). Similarly, there are no perfect square factors, so we can't simplify it either.

Step 2: Apply the division rule for square roots.

When dividing square roots, we divide the numbers under the square roots and keep the square roots separate.

Thus, 2√65 ÷ √5 equals (2/1) × (√65/√5)

Step 3: Simplify the fraction.

We can simplify the fraction (2/1) × (√65/√5) by multiplying the numerator and denominator separately.

2/1 × √65/√5 = (2 × √65)/(1 × √5) = (2√65)/(√5)

Step 4: Rationalize the denominator.

To rationalize the denominator, we multiply the top and bottom of the fraction by the conjugate of the denominator.

The conjugate of √5 is -√5.

(2√65)/(√5) × (-√5)/(-√5) = (-2√65√5)/(√5 × √5) = (-2√(65 × 5))/(√(5 × 5)) = (-2√325)/5

So, 2√65 ÷ √5 equals -2√325/5.