Gr 11 Math Ch 1: Rational Exponents and Surds
37 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the value of $r$ if $r^3 = 27$?

  • $3$ (correct)
  • $\sqrt[3]{27}$
  • $9$
  • $-3$

    • What is the value of $a^{rac{2}{3}}$ if $a = 8$?

  • $\sqrt{8^2}$
  • $4$
  • $\sqrt[3]{8^2}$ (correct)
  • $2$

    • What is the value of $\sqrt[4]{81}$?

  • $3$ (correct)
  • $-3$
  • $9$
  • $\sqrt{81}$

    • What is the value of $(\sqrt{16})^2$?

    <p>$16$</p> Signup and view all the answers

    What is the value of $\sqrt{12} imes \sqrt{3}$?

    <p>$2\sqrt{3}$</p> Signup and view all the answers

    What is the value of $rac{\sqrt{50}}{\sqrt{2}}$?

    <p>$rac{5}{2}$</p> Signup and view all the answers

    What is the value of $\sqrt[3]{27} imes \sqrt[3]{8}$?

    <p>$\sqrt[3]{216}$</p> Signup and view all the answers

    What is the value of $2^{rac{3}{2}}$?

    <p>$\sqrt{2^3}$</p> Signup and view all the answers

    What is the definition of $r$ in terms of $a$ when $r^n = a$?

    <p>$r = \sqrt[n]{a}$</p> Signup and view all the answers

    What is the value of $a^{rac{m}{n}}$ when $a > 0$, $m, n \in \mathbb{Z}$, and $n eq 0$?

    <p>$\sqrt[n]{a^m}$</p> Signup and view all the answers

    What is the definition of a surd?

    <p>A radical resulting in an irrational number</p> Signup and view all the answers

    What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?

    <p>$\sqrt[n]{ab}$</p> Signup and view all the answers

    What is the purpose of rationalizing the denominator?

    <p>To eliminate the surd from the denominator</p> Signup and view all the answers

    What is the result of raising $\sqrt[n]{a}$ to the power of $m$?

    <p>$a^{rac{m}{n}}$</p> Signup and view all the answers

    What is the value of $a^{-rac{1}{n}}$?

    <p>$rac{1}{\sqrt[n]{a}}$</p> Signup and view all the answers

    What is the result of dividing $\sqrt[n]{a}$ by $\sqrt[n]{b}$?

    <p>$\sqrt[n]{rac{a}{b}}$</p> Signup and view all the answers

    If $a > 0$ and $m, n \in \mathbb{Z}$, then what is the value of $a^{rac{m}{n}}$ in terms of radicals?

    <p>$\sqrt[n]{a^m}$</p> Signup and view all the answers

    What is the value of $\sqrt[3]{a^2} imes \sqrt[3]{a^4}$?

    <p>$a^{rac{6}{3}}$</p> Signup and view all the answers

    What is the value of $rac{\sqrt{a}}{\sqrt{b}}$?

    <p>$\sqrt{rac{a}{b}}$</p> Signup and view all the answers

    What is the value of $\sqrt{a} imes \sqrt[3]{a^2}$?

    <p>$a^{rac{3}{2}}$</p> Signup and view all the answers

    What is the purpose of rationalizing the denominator of a fraction?

    <p>To eliminate the surd from the denominator</p> Signup and view all the answers

    What is the value of $\left(\sqrt{a} ight)^3$?

    <p>$a^3$</p> Signup and view all the answers

    What is the value of $\sqrt[4]{a^3}$?

    <p>$a^{3/4}$</p> Signup and view all the answers

    What is the value of $\sqrt{a} imes \sqrt{b}$?

    <p>$\sqrt{a imes b}$</p> Signup and view all the answers

    What is the value of $a^{rac{3}{2}}$ when $a = 16$?

    <p>8</p> Signup and view all the answers

    What is the value of $\sqrt[4]{x^2}$ when $x = 9$?

    <p>3</p> Signup and view all the answers

    What is the value of $rac{\sqrt{50}}{\sqrt{10}}$?

    <p>$\sqrt{5}$</p> Signup and view all the answers

    What is the value of $a^{rac{2}{3}}$ when $a = 27$?

    <p>9</p> Signup and view all the answers

    What is the value of $\sqrt[3]{x^2}$ when $x = 8$?

    <p>2</p> Signup and view all the answers

    What is the value of $rac{\sqrt[3]{a^2}}{\sqrt[3]{a}}$ when $a = 27$?

    <p>3</p> Signup and view all the answers

    What is the value of $a^{rac{3}{4}}$ when $a = 16$?

    <p>8</p> Signup and view all the answers

    What is the value of $\sqrt{x^2}$ when $x = 4$?

    <p>4</p> Signup and view all the answers

    What is the value of $a^{\frac{2}{3}}$ when $a = 27$?

    <p>$3\sqrt{3}$</p> Signup and view all the answers

    What is the purpose of rationalizing the denominator of a fraction?

    <p>To eliminate the surd from the denominator</p> Signup and view all the answers

    What is the value of $\sqrt[3]{a^2} \times \sqrt[3]{a^4}$ when $a > 0$?

    <p>$a^{2}$</p> Signup and view all the answers

    What is the value of $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ when $a, b > 0$ and $n \in \mathbb{Z}$?

    <p>$\sqrt[n]{\frac{a}{b}}$</p> Signup and view all the answers

    What is the definition of a surd?

    <p>A radical resulting in an irrational number</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser