Question

Which number is a rational number

Answer 1

square root of 49 i think

Answer 2

Answer:

$\sqrt{ \frac{36}{16} }$

Step-by-step explanation:

A rational number is one that can be expressed as a fraction.

• $\sqrt{ \frac{36}{6} } = \sqrt{6}$
• sqrt(6) is irrational.

Therefore, top left and right and irrational.

Bottom left:

• $\sqrt{ \frac{36}{16} } = \frac{ \sqrt{36} }{ \sqrt{16} } = \frac{6}{4} = \frac{3}{2}$
• Very obviously already in a fractional form making it rational.

Bottom right:

• $\sqrt{ \frac{16}{6} } = \frac{ \sqrt{16} }{ \sqrt{6}} = \frac{4}{ \sqrt{6} } = \frac{4 \sqrt{6} }{6} = \frac{2 \sqrt{6} }{3}$
• We already established that the sqrt(6) is not rational, so this expression is also irrational.