mais younger brother tells her that $\frac{10...
mais younger brother tells her that $\frac{10}{7}$ is equal to $sqrt{2}$. mai knows this cant be right, because $\frac{10}{7}$ is rational and $sqrt{2}$ is irrational. write an explanation that mai could use to convince her brother that $\frac{10}{7}$ cannot be the square root of 2.
Answer
# Brief Explanations:
Rational numbers can be written as a fraction $\frac{p}{q}$ ($p,q$ are integers, $q\neq0$). The square - root of a non - perfect - square number like 2 is irrational. If $\frac{10}{7}$ were $\sqrt{2}$, then squaring $\frac{10}{7}$ should give 2. But $(\frac{10}{7})^2=\frac{100}{49}\neq2$. Also, rational numbers have either terminating or repeating decimal expansions, while irrational numbers have non - terminating and non - repeating decimal expansions. $\frac{10}{7}=1.\overline{428571}$ and $\sqrt{2}=1.414213562373095\cdots$
# Answer:
$\frac{10}{7}$ cannot be $\sqrt{2}$ because $(\frac{10}{7})^2=\frac{100}{49}\neq2$, and they have different types of decimal expansions (rational vs. irrational).