Which shows the expressions in the order they would appear on a number line from least to greatest?
17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3
3 to the power of 3, square root of 30, square root of 15, square root of 6, 17 over 9
3 to the power of 3, square root of 6, square root of 15, 17 over 9, square root of 30
17 over 9, square root of 30, square root of 15, 3 to the power of 3, square root of 6
17/9, √6, √15, √30, 3^3
To find the expressions in order from least to greatest, we will compare the numerical values of each expression.
First, let's simplify each expression:
1) 3 to the power of 3 = 3^3 = 27
2) Square root of 30 ≈ 5.48
3) Square root of 15 ≈ 3.87
4) 17 over 9 ≈ 1.89
5) Square root of 6 ≈ 2.45
Now let's arrange these values in ascending order:
1. 17 over 9 ≈ 1.89
2. Square root of 6 ≈ 2.45
3. Square root of 15 ≈ 3.87
4. 3 to the power of 3 = 27
5. Square root of 30 ≈ 5.48
Therefore, the expressions in the correct order from least to greatest are:
17 over 9, square root of 6, square root of 15, 3 to the power of 3, square root of 30.
To determine the order of these expressions from least to greatest, we need to compare their values.
Let's start by considering the given expressions:
17/9 ≈ 1.89
√6 ≈ 2.45
√15 ≈ 3.87
√30 ≈ 5.48
3^3 = 3 × 3 × 3 = 27
Now, we can compare the values:
1.89 is the least among these values because it is the smallest decimal number.
Next is 2.45, followed by 3.87, 5.48, and finally 27.
Therefore, the expressions in the order they would appear on a number line from least to greatest are:
17/9, √6, √15, √30, 3^3
So, the correct answer is:
17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3.