Question

Which number is a rational number? The square root of 16/6, the square root of 36/6, the square root of 36/16, or the square root of 6

Answer 1

Answer:

36/16

Step-by-step explanation:

Answer 2

Answer:

The square root of 36/16, that is 1,5

Step-by-step explanation:

First let's see square root of 16/6!

$\sqrt{\frac{16}{6} }$

the top part of the radical is 4 and the bottom part is square root of 6! that is not a rational number because rational number can be written as the quotient of two whole numbers!

$\sqrt{\frac{16}{6} }=\frac{\sqrt{16} }{\sqrt{6} } =\frac{4}{\sqrt{6}}$

Then let's take a look at the square root of 36/6,

$\sqrt{\frac{36}{6} } =\frac{\sqrt{36} }{\sqrt{6} } =\frac{6}{\sqrt{6} }$

due to the fact that it has a root that is not written as a whole number in the denominator, then it is not a rational number!

Now square root of 6

$\sqrt{6}$

Certainly this square root can be calculated and is equal to 2,449489... but because it has infinite digits after the comma, it can't be written as a quotient!

Finally, the square root of 36/16

$\sqrt{\frac{36}{16} } =\frac{\sqrt{36} }{\sqrt{16} } =\frac{6}{4}=\frac{3}{2} =1,5$

the square root of 36/16 can be written as a quotient, as it is shown!

Actually it is equal to 1,5, that is the quotient of two whole number: 3/2!

So the square root of 36/16 is our answer!