Question

Which of the following is irrational?
options:

3.6363636363636363...

√3 over 4

−7 and 8 over 37

52.781654292

Answer 1

Estimate the value of 6 x √2 . Which of the following choices is the best estimate?

options:

8.4
8.4

7.1
7.1

6.4
6.4

9.8

Answer 2

To determine which of the options is irrational, we will analyze each one:

1. **3.6363636363636363...**: This is a repeating decimal. Any repeating decimal can be expressed as a fraction, therefore this number is **rational**.

2. **√3 over 4**: The square root of 3 (√3) is an irrational number. Since the division of an irrational number by a non-zero rational number (4) remains irrational, √3/4 is **irrational**.

3. **−7 and 8 over 37**: This notation seems to represent a mixed number, which can be written as \(-7 + \frac{8}{37}\). Both integers and fractions (like 8/37) are rational. Therefore, this expression is **rational**.

4. **52.781654292**: This is a finite decimal, which can also be expressed as a fraction. Hence, this number is **rational**.

Based on the analysis, the option that is irrational is:

**√3 over 4**.