QuestionDetermine if the product $\sqrt{12} \times \frac{3}{8}$ is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We are asked to determine if the result of the product is a rational or an irrational number. . A rational number is a number that can be expressed as the quotient of two integers, with the denominator not equal to zero.
3. An irrational number cannot be expressed as the ratio of two integers.
4. The square root of a non-perfect square is an irrational number.

STEP 2

First, let's simplify the square root.
$\sqrt{12} = \sqrt{4 \times} = \sqrt{4} \times \sqrt{} =2\sqrt{}$

STEP 3

Now, let's multiply the simplified square root by the fraction.
$2\sqrt{3} \times \frac{3}{8} = \frac{6\sqrt{3}}{8}$

STEP 4

We can simplify the fraction further by dividing the numerator and the denominator by their greatest common divisor, which is2.
$\frac{6\sqrt{3}}{8} = \frac{3\sqrt{3}}{4}$

STEP 5

Now, let's determine if the result is a rational or an irrational number. The number $\sqrt{3}$ is an irrational number, and the product of a rational number ( $\frac{3}{4}$ ) and an irrational number ( $\sqrt{3}$ ) is an irrational number. Therefore, the result of the product is an irrational number.
The result of the product $\sqrt{12} \times \frac{3}{8}$ is an irrational number.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms