What type of number will result from the expression 19−−√ −3/2

Question

(1 point)

a whole number

a rational number

an irrational number

an integer

Answer 1

To evaluate the expression \( \sqrt{19} - \frac{3}{2} \):

1. The term \( \sqrt{19} \) is an irrational number because it cannot be expressed as a fraction of two integers.
2. The term \( \frac{3}{2} \) is a rational number because it can be expressed as a fraction of two integers.

When you subtract a rational number from an irrational number, the result is always irrational.

Therefore, the answer is:

an irrational number.

Answer 2

Find the product of 12−−√ and 5/6

. What type of number is it?(1 point)
Responses
4.1569...; an irrational number
4.1569...; an irrational number
4.2974...; an irrational number
4.2974...; an irrational number
2.8867...; an irrational number
2.8867...; an irrational number
2.6307...; an irrational number

Answer 3

Let’s calculate the product of \( \sqrt{12} \) and \( \frac{5}{6} \):

1. First, we evaluate \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

2. Now, find the product: \[ 2\sqrt{3} \cdot \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3} \]

3. Since \( \sqrt{3} \) is an irrational number, any product or quotient involving \( \sqrt{3} \) (like \( \frac{5\sqrt{3}}{3} \)) is also irrational.

To find the approximate value of \( \frac{5\sqrt{3}}{3} \):

• The value of \( \sqrt{3} \) is approximately \( 1.732 \): \[ \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867... \]

Based on these calculations, the product \( \frac{5\sqrt{3}}{3} \approx 2.8867... \) is an irrational number.

Therefore, the correct response is:

2.8867...; an irrational number.