the expression 6 times radical 20 divided by 3 times radical 5 is equvilent to

1. 3 radical 15
2. 2 radical 15
3. 8
4. 4

6√20/3√5

= 6√4√5/3√5
= 6x2√5/3√5
= 12/3
= 4

To simplify the expression (6√20) / (3√5), we need to simplify both the numerator and the denominator separately, and then divide the two simplified expressions.

Let's start with the numerator:
6 * √20 = 6 * √(4 * 5) = 6 * (√4 * √5) = 6 * (2 * √5) = 12 * √5

Now let's simplify the denominator:
3 * √5 = 3 * √5

Now we can divide the numerator by the denominator:
(12 * √5) / (3 * √5)

Since the √5 terms in the numerator and denominator cancel each other out, we are left with:
(12 / 3)

Simplifying further, we find that the expression is equivalent to:
4

Therefore, the correct answer is option 4.

To simplify the expression, let's break it down step by step:

1. Start with the expression: 6 times radical 20 divided by 3 times radical 5.

2. Simplify the radicands (the numbers inside the radical sign):
- The square root of 20 simplifies to 2 times the square root of 5.
- The square root of 5 remains unchanged.

3. Rewrite the expression using the simplified radicands:
- 6 times (2 times radical 5) divided by 3 times radical 5.

4. Multiply the numbers outside the radical sign:
- 6 times 2 is equal to 12.

5. Multiply the radicands:
- radical 5 times radical 5 is equal to 5.

6. Simplify the expression further:
- 12 times radical 5 divided by 3 times radical 5.

7. Divide the numbers outside the radical sign:
- 12 divided by 3 is equal to 4.

8. Divide the radicands:
- radical 5 divided by radical 5 is equal to 1.

9. The simplified expression becomes:
- 4 times 1, which is equal to 4.

Therefore, the equivalent of the expression 6 times radical 20 divided by 3 times radical 5 is 4. So, the answer is option 4.