Algebra Class: Surds and Indices
26 Questions
0 Views

Algebra Class: Surds and Indices

Created by
@SmittenBoolean

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the result of multiplying the surds $2 \times 3$?

  • $4$
  • $8$
  • $6$ (correct)
  • $5$
  • The square root of $25$ simplifies to $5$.

    True

    What is the simplified form of $\sqrt{200}$?

    10\sqrt{2}

    $2 + 3\sqrt{5}$ simplifies to _________ when there is another term with $\sqrt{5}$ to add.

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

    Match the following operations with their results:

    <p>$\sqrt{12}$ = $2\sqrt{3}$ $10 \div 2$ = $5$ $\sqrt{45}$ = $3\sqrt{5}$ $\sqrt{16}$ = $4$</p> Signup and view all the answers

    What is the result of the operation $3^2 - 8$?

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

    What is the result of dividing the surd $12 \div 6$?

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

    What are the results of adding $5 + 3\sqrt{5}$?

    <p>5 + 3\sqrt{5}</p> Signup and view all the answers

    $4^3 ÷ 2^6$ equals $24^2$.

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

    What is the simplified form of $15x^3 ÷ 3x^2$?

    <p>5x</p> Signup and view all the answers

    Surds can only be simplified if they contain square numbers.

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

    The expression $x^{-2}$ can be rewritten in ordinary form as ___.

    <p>1/x²</p> Signup and view all the answers

    Match the following expressions with their equivalent forms:

    <p>x^0 = 1 x^3 = x<em>x</em>x x^-1 = 1/x x^(1/2) = √x</p> Signup and view all the answers

    What is the result of the operation $5 imes 5^2$?

    <p>125</p> Signup and view all the answers

    The expression $x^2 ÷ x^2$ is equal to 1 for any non-zero x.

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

    What is the result of $32 - 48 - 75$?

    <p>-91</p> Signup and view all the answers

    What is the ordinary form of $x^{1}$?

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

    The expression $x^{2}$ is equivalent to $x imes x$ in ordinary form.

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

    What is the ordinary form of $x^{ rac{1}{2}}$?

    <p>√x</p> Signup and view all the answers

    The expression $x^{1/3}$ represents the __________ of x.

    <p>cube root</p> Signup and view all the answers

    Match the ordinary form expressions with their index form expressions:

    <p>1 = A: $x^{0}$ 2 = B: $x^{1}$ 4 = C: $x^{2}$ 8 = D: $x^{3}$</p> Signup and view all the answers

    Which of the following is the index form of the expression $x imes x imes x$?

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

    The expression $x^{ rac{1}{4}}$ can be expressed as $x^{4}$ in ordinary form.

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

    What is the ordinary form of $x^{2}$?

    <p>x squared</p> Signup and view all the answers

    The index form of $4$ is __________.

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

    Match the following index forms with their ordinary equivalents:

    <p>$x^{3}$ = A: $x imes x imes x$ $x^{ rac{1}{2}}$ = B: √x $x^{2}$ = C: $x imes x$ $x^{0}$ = D: 1</p> Signup and view all the answers

    Study Notes

    Surds

    • Multiplying surds: Multiplying surds involves multiplying the values inside the radical symbol. For example, 2√3 × √10 = √60.
    • Dividing surds: Dividing surds involves dividing the values inside the radical symbol. For example, √10 ÷ √2 = √5.
    • Simplifying surds: Simplifying surds involves taking out perfect square numbers from inside the radical symbol and finding their root. For example, √4a = √(4 × a) = 2√a.
    • Adding and subtracting surds: Adding and subtracting surds requires the same surd to be present in both terms. For example, √b + 2√b = 3√b.

    Indices

    • Multiplying indices: When multiplying indices with the same base, add the exponents. For example, x * x = x².
    • Dividing indices: When dividing indices with the same base, subtract the exponents. For example, x ÷ x = x⁻¹.
    • Powers of indices: When raising a power to another power, multiply the exponents. For example, (x²)³ = x⁶.
    • Negative indices: A negative index represents the reciprocal of the base raised to the positive value of the index. For example, x⁻¹ = 1/x.
    • Fractional indices: A fractional index indicates taking the root of the base. For example, x½ = √x.
    • Power of zero: Any base raised to the power of zero is equal to one. For example, x⁰ = 1.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Description

    Test your understanding of surds and indices in this algebra quiz. This quiz covers multiplying, dividing, simplifying surds, and the rules for handling indices. Challenge yourself to apply these concepts to various problems.

    More Like This

    Surds and Indices Quiz
    12 questions
    Indices and Surds
    30 questions

    Indices and Surds

    NourishingRoseQuartz avatar
    NourishingRoseQuartz
    Algebra Indices and Surds
    9 questions

    Algebra Indices and Surds

    CourageousIntegral avatar
    CourageousIntegral
    Surds and Indices Test
    5 questions

    Surds and Indices Test

    EliteEucalyptus avatar
    EliteEucalyptus
    Use Quizgecko on...
    Browser
    Browser