Evaluate the expression 5x−2^3/2

Question

when x = 6(1 point)
Responses

10
10

11
11

12
12

13

the answer is 27

Answer 1

To evaluate the expression \(5x - 2^{3/2}\) when \(x = 6\), follow these steps:

1. Substitute \(x\) with 6: \[ 5(6) - 2^{3/2} \]

2. Calculate \(5(6)\): \[ 30 \]

3. Next, calculate \(2^{3/2}\): \[ 2^{3/2} = (2^3)^{1/2} = 8^{1/2} = \sqrt{8} = 2\sqrt{2} \]

   To be more precise: \[ 2^{3/2} = 2 \cdot \sqrt{2} \approx 2 \cdot 1.414 \approx 2.828 \]

4. Now, we substitute back into the expression: \[ 30 - 2\sqrt{2} \]

5. Since \(2\sqrt{2}\) is approximately \(2.828\), we do: \[ 30 - 2.828 \approx 27.172 \]

Thus, when rounded, this value does indeed come close to 27. However, the integer part is 27, as you indicated in your last statement. Therefore, for practical purposes, you can say that the evaluated expression rounds to 27 when \(x = 6\).

So, the answer is approximately \(27\).