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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
2.73 Radicals

In
m is the index or order
is the radical or square root sign
a is the radicand

Radicals involve the use of the radical sign (√). Sometimes these are also called surds.
  • Square root:
    A number that must be multiplied times itself to equal a given number. The square root of a is written √a or a1/2.

  • Cube root:
    A number that must be multiplied times itself three times to equal a given number. The cube root of a is written or 3√a or a1/3.

  • 4th root, 5th root or nth root:
    The number that must be multiplied times itself m times to equal a given value. The mth root of a is written m√a or a1/m.
    Example, 5√32 = 2 since 25 = 32.
    Note: When m = 2 an mth root is called a square root.
    When m = 3 an mth root is called a cube root.
    When m = 4 an mth root is called fourth root.
    When m = 5 an mth root is called fifth root.
    and so on......
    If m is even and a is negative, then n√x is non real.

A surd or a radical is an expression containing a root with an irrational solution that can not be expressed exactly.
For example: √3 = 1.732050808......

For any real number a and any integer m, m>1, the principal nth root of a can be described as follows:
If a > 0 then is a positive real number.
If a = 0, then is zero.
If a < 0, and n is odd, then is a negative real number.
If a < 0, and n is even, then is not a real number.

Example:
53
3 is a positive rational number
53 is a surd with 5th order.


Directions: Choose the correct answer. Also write at least 10 examples of your own for square root, cube root and nth root.
Q 1: 6-1 is a real number.
True
False

Q 2: The index in 3 is ____.
Answer:

Q 3: 0.09 = ____
0.3
3

Q 4: The order of the surd in 37 is ______
Answer:

Q 5: 310 is a radical expression.
True
False

Q 6: The index in 5x4 is ____.
Answer:

Q 7: The order of the surd in 123 is ___.
Answer:

Q 8: The radicand in 532 is 5 is ___.
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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