Question

Which expression is rational?
6.27316543222718…
square root of 2
square root of 14.
square root of 49

Answer 1

@Michele_Laino

Answer 2

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:
\[\Large \sqrt {49} = 7 = \frac{7}{1}\]

Answer 3

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:
\[\Large R = \frac{m}{n},\quad m,n \in \mathbb{Z},\;n \ne 0\]

Answer 4

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

Answer 5

but they both can be rational

Answer 6

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

Answer 7

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

Answer 8

oh

Answer 9

oh i see they cant be expressed as a fraction

Answer 10

yes! So what is the right option?

Answer 11

\[\sqrt{49}\]

Answer 12

that's right!