Problemas

Which of the following multiplication problems yield a product that is a mional number? Seluct TWO that apply. -2times (5)/(7) B. (2)/(5)times 3sqrt (2) v C 2pi times (1)/(3) D. 5times -3
Solución

Diegoprofessionell · Tutor durante 6 años

4.7 (182 votos)
Responder
To determine which multiplication problems yield a product that is an irrational number, we need to understand the definition of an irrational number. An irrational number is a number that cannot be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Irrational numbers have non-repeating, non-terminating decimal expansions.<br /><br />Let's analyze each option:<br /><br />A. \( -2 \times \frac{5}{7} \)<br />\[ -2 \times \frac{5}{7} = \frac{-10}{7} \]<br />This is a rational number because it can be expressed as a fraction.<br /><br />B. \( \frac{2}{5} \times 3\sqrt{2} \)<br />\[ \frac{2}{5} \times 3\sqrt{2} = \frac{6\sqrt{2}}{5} \]<br />This is an irrational number because \( \sqrt{2} \) is irrational, and multiplying an irrational number by a rational number (other than zero) results in an irrational number.<br /><br />C. \( 2\pi \times \frac{1}{3} \)<br />\[ 2\pi \times \frac{1}{3} = \frac{2\pi}{3} \]<br />This is an irrational number because \( \pi \) is irrational, and multiplying an irrational number by a rational number (other than zero) results in an irrational number.<br /><br />D. \( 5 \times -3 \)<br />\[ 5 \times -3 = -15 \]<br />This is a rational number because it can be expressed as a fraction.<br /><br />Therefore, the correct answers are:<br />B. \( \frac{2}{5} \times 3\sqrt{2} \)<br />C. \( 2\pi \times \frac{1}{3} \)
Haz clic para calificar: