## anonymous one year ago Which expression is rational? 6.27316543222718… square root of 2 square root of 14. square root of 49

1. anonymous

@Michele_Laino

2. Michele_Laino

hint: the first number is an number with an infinity of decimal figures, so it is an irrational number, furthermore, we have 49=7^2, so: $\Large \sqrt {49} = 7 = \frac{7}{1}$

3. Michele_Laino

hint: a rational number R, is a number which can be written as a ratio between two integers, say m, and n, and such that n is different from zero, namely: $\Large R = \frac{m}{n},\quad m,n \in \mathbb{Z},\;n \ne 0$

4. Michele_Laino

$$\Large \sqrt 2 ,\quad \sqrt {14}$$ are not expressible like a ratio above

5. anonymous

but they both can be rational

6. Michele_Laino

whereas: $\Large \sqrt {49} = 7 = \frac{7}{1}$ is expressible as a ratio between 7 and 1

7. Michele_Laino

no, $$\large \sqrt 2 ,\quad \sqrt {14}$$ are both irrational

8. anonymous

oh

9. anonymous

oh i see they cant be expressed as a fraction

10. Michele_Laino

yes! So what is the right option?

11. anonymous

$\sqrt{49}$

12. Michele_Laino

that's right!