MATH SOLVE

3 months ago

Q:
# What number can you multiply by −√2 to get a rational number? Select each correct answer. A. 12B. √2C. 0D. 2

Accepted Solution

A:

we know thatA rational number is any number that can be expressed as a ratio of two integerssocase A) [tex]12[/tex][tex]-\sqrt{2}*(12)=-12 \sqrt{2}[/tex] -----> is not a rational numbercase B) [tex]\sqrt{2}[/tex][tex]-\sqrt{2}*(\sqrt{2})=-4[/tex] -----> is a rational numberbecause can be written as a quotient of two integer numbers. For example[tex]-4=\frac{-8}{2}[/tex]case C) [tex]0[/tex][tex]-\sqrt{2}*(0)=0[/tex] -----> is a rational numberbecause can be written as a quotient of two integer numbers. For example[tex]0=\frac{0}{1}[/tex]case D) [tex]2[/tex][tex]-\sqrt{2}*(2)=-2 \sqrt{2}[/tex] -----> is not a rational numberthereforethe answer is[tex]\sqrt{2}[/tex][tex]0[/tex]