Order the radicals from smallest to largest 5√3 , 2√15 , 4√5 , 8 , 6√2
Hmmm. 8 = 8.0
2√15 = 7.74
I don't think they're in order yet.
Apologies for the confusion. Let's reorder the radicals from smallest to largest:
2√15, 4√5, 5√3, 6√2, 8
still wrong. Since √5 > 2, 4√5 > 8
To order the given radicals from smallest to largest, we need to simplify them and compare their values.
1. Let's start by simplifying each radical:
- 5√3 cannot be simplified further since 3 is not a perfect square.
- 2√15 can be simplified as follows:
√15 = √(3 * 5) = √3 * √5 = √3√5
Therefore, 2√15 = 2√3√5
- 4√5 cannot be simplified further since 5 is not a perfect square.
- 8 is already in its simplified form.
- 6√2 cannot be simplified further since 2 is not a perfect square.
2. Now, let's compare the simplified radicals:
- 2√3√5 and 4√5: Since both radicals have the same base (√5), we can compare their coefficients. The coefficient of 2√3√5 is 2, and the coefficient of 4√5 is 4. Therefore, 2√3√5 is smaller than 4√5.
- 4√5 and 5√3: Since 5 is greater than 4, 5√3 is larger than 4√5.
- 5√3 and 6√2: Since 6 is greater than 5, 6√2 is larger than 5√3.
- 6√2 and 8: Since 8 is greater than 6, 8 is larger than 6√2.
3. Putting them in order from smallest to largest:
2√3√5, 4√5, 5√3, 6√2, 8
To order the radicals from smallest to largest, we need to compare their values. Let's simplify each radical expression to determine their exact values:
1. Simplifying 5√3: Since √3 cannot be simplified further, we keep it as it is. Thus, 5√3 remains the same.
2. Simplifying 2√15: The square root of 15 can be simplified as the product of the square root of 3 and the square root of 5 (√(3*5) = √15). Therefore, 2√15 can be written as 2(√3)(√5). Multiplying the coefficients, we get 2(√15), which is the simplified form.
3. Simplifying 4√5: The square root of 5 cannot be simplified further, so we keep it as it is. Hence, 4√5 remains unchanged.
4. Simplifying 6√2: Similarly, the square root of 2 cannot be simplified further, so we keep it as it is. Thus, 6√2 remains the same.
Now, let's compare the simplified radical expressions:
- 8: 8 is just a number and does not contain any radicals.
- 2√15: We simplified it as 2(√15).
- 4√5: We kept it unchanged as 4√5.
- 6√2: We kept it in its original form as 6√2.
- 5√3: It was already in its simplest form, so we kept it unchanged.
Arranging them from smallest to largest:
8, 2(√15), 4√5, 6√2, 5√3.
Thus, the order from smallest to largest is 8, 2(√15), 4√5, 6√2, 5√3.
8, 4√5, 6√2, 5√3, 2√15
You're right, my apologies for the mistake. Here is the correct order from smallest to largest:
2√15, 5√3, 6√2, 4√5, 8