Algebra Class - Perfect Squares
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Questions and Answers

Which of the following numbers is a perfect square?

  • 121 (correct)
  • 200
  • 32
  • 50

    • The number 64 is a perfect square.

    False

    What is the approximate value of the square root of 84 to the nearest tenth?

    9.2

    The cube of an integer is called a _________________ ________________.

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

    Match the following numbers to their square roots:

    <p>1 = 1 4 = 2 9 = 3 16 = 4</p> Signup and view all the answers

    What is the opposite of cubing a number?

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

    How many cube roots do all integers have?

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

    What number(s) can you cube to get 8? __________, __________.

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

    The square of an integer is called a _________________ ________________.

    <p>perfect square</p> Signup and view all the answers

    What is the square root of 49?

    <p>7</p> Signup and view all the answers

    Negative numbers have positive square roots.

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

    What number(s) can you square to get 16?

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

    Positive numbers have ________ square roots.

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

    Match the following terms with their definitions:

    <p>Perfect Square = A number that is the square of an integer Square Root = A value that, when multiplied by itself, gives the original number Radical Notation = The symbol used to denote square roots Negative Square Root = The square root of a number that is less than zero</p> Signup and view all the answers

    Which radical notation indicates the principal square root of a number?

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

    What number only has one square root?

    <p>0</p> Signup and view all the answers

    Which two consecutive integers contain the square root of 95?

    <p>9 and 10</p> Signup and view all the answers

    The cube root of 729 is 9.

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

    What is the cube root of 125?

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

    The square root of a non-zero integer has ________ square roots.

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

    Which of the following values is a perfect cube?

    <p>1,000</p> Signup and view all the answers

    The number 48 is a perfect cube.

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

    Match the following numbers with their corresponding properties:

    <p>27 = Perfect Cube 1 = Perfect Cube 216 = Perfect Cube 90 = Not a Perfect Cube</p> Signup and view all the answers

    Estimate the square root of 372 to the nearest tenth.

    <p>19.3</p> Signup and view all the answers

    What is the correct form of the number 540 in scientific notation?

    <p>5.40 × 10^2</p> Signup and view all the answers

    The number 0.00982 is correctly written in scientific notation.

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

    What is the exponent when converting the number 937,000 to scientific notation?

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

    If the decimal was moved ___________, the exponent is negative.

    <p>to the left</p> Signup and view all the answers

    Which of the following is an incorrect representation of scientific notation?

    <p>85.1 × 10^6</p> Signup and view all the answers

    Match the number to its scientific notation:

    <p>1,852,000 = 1.852 × 10^6 76,820 = 7.682 × 10^4 4,671 = 4.671 × 10^3 0.0000014 = 1.4 × 10^-6</p> Signup and view all the answers

    The number 6.7 × 10^-2 is a valid scientific notation representation.

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

    How would you write the number 0.00000000725 in scientific notation?

    <p>7.25 × 10^-9</p> Signup and view all the answers

    What number can be cubed to result in -8?

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

    The cube root of -27 is -3.

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

    What is the cube root of 512?

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

    The cube root of a negative number will always yield a ______ result.

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

    Match the following numbers with their respective cube roots:

    <p>-27 = -3 343 = 7 512 = 8 -8 = -2</p> Signup and view all the answers

    Which of the following is a perfect square?

    <p>81</p> Signup and view all the answers

    The number 64 is a perfect square.

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

    Circle all the perfect squares from the following list: 50, 81, 289, 360.

    <p>81, 289</p> Signup and view all the answers

    Study Notes

    Perfect Squares and Cube Roots

    • A perfect square is the square of an integer.
    • First 10 perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
    • To find square roots, determine the opposite of squaring a number.
    • Positive numbers have real square roots; negative numbers have no real square roots.
    • The square root of 16 is 4 (or -4).
    • The radical sign (√x) denotes the principal square root of x; -√x indicates the negative square root.
    • A non-perfect square does not yield an integer when square rooted.

    Estimating Square Roots

    • Identify two consecutive integers between which a square root lies.
    • Approximate square roots to the nearest tenth (e.g., √84 between 9 and 10).

    Perfect Cubes

    • A perfect cube is the cube of an integer.
    • First 10 perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
    • Cube roots denote finding the opposite of cubing a number.
    • All integers have one cube root; for instance, cube roots for 8 yield 2, and for -8 yield -2.

    Understanding Square Roots

    • Every non-zero integer has two square roots (positive and negative), but only one cube root because cubing can only yield a specific value without ambiguity.

    Scientific Notation

    • Scientific notation simplifies the writing of very large or very small numbers.
    • Written in the form a × 10^n, where 1 ≤ a < 10.
    • Steps for conversion to scientific notation:
      • Move the decimal point to obtain a number between 1 and 10.
      • The exponent reflects the number of places moved; right move indicates a negative exponent, left indicates positive.
    • Ensure written numbers adhere to scientific notation rules, correcting as necessary.

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    Description

    Test your understanding of perfect squares in this Algebra class quiz. Explore main ideas, examples, and questions to reinforce your learning on the topic of integers and their squares.

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