Question

2 √65 / √5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (2√65) / √5, you can first simplify the numerator and denominator separately.

In the numerator (2√65), you can simplify the square root of 65:
√65 = √(5 × 13) = √5 × √13 = √5√13 = √(5 × 13) = √(65) = √(5^2 × 13) = 5√13

So, the numerator becomes 2 × 5√13 = 10√13.

In the denominator (√5), you don't need to do anything else as it is already simplified.

Therefore, (2√65) / √5 simplifies to 10√13 / √5.

Answer 2

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

To simplify the expression (2√65 / √5), you can follow these steps:

Step 1: Simplify the denominator:
√5 = √(5) = √(5 * 1) = √5 * √1 = √5

Step 2: Rewrite the expression using the simplified denominator:
2√65 / √5 = 2√65 / (√5)

Step 3: Rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator (√5):
2√65 / (√5) * (√5) / (√5) = (2√65 * √5) / (√5 * √5)

Step 4: Simplify the numerator:
2√65 * √5 = 2 * √(65 * 5) = 2 * √(325) = 2√325

Step 5: Simplify the denominator:
√5 * √5 = (√5)^2 = 5

Step 6: Rewrite the expression using the simplified numerator and denominator:
(2√65 * √5) / (√5 * √5) = (2√325) / 5

Therefore, the simplified form of (2√65 / √5) is (2√325) / 5.

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression (2√65) / √5, we can follow these steps:

Step 1: Simplify the numerator (2√65):

- First, we can simplify the square root of 65. Since there are no perfect square factors of 65, we cannot simplify it further.

Step 2: Simplify the denominator (√5):

- The square root of 5 cannot be simplified further because 5 is not a perfect square.

Step 3: Divide the numerator by the denominator:

- We can rewrite the expression as (2√65) * (1/√5).
- To divide by a fraction, we multiply by its reciprocal. Therefore, we can rewrite it as (2√65) * (√5/1).
- When multiplying two square roots with the same radicand, we multiply the coefficients outside the square roots and the radicands inside the square roots. Therefore, we get 2 * √(65 * 5).
- Simplifying further, 65 * 5 = 325.
- Finally, the simplified expression is 2√325.

So, the answer is 2√325.