Mathematics 1201 Unit 2: Powers and Roots
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Mathematics 1201 Unit 2: Powers and Roots 3.1: Factors and Multiples of Whole Numbers Prime Factorization: the number written as a product of its prime factors Greatest Common Factor: the GCF of two or more numbers is the greatest factor the numbers have in common. Least Common Multiple: the LCM of two or more numbers is the least number that is divisible by each number. EXAMPLE: Write the prime factorization of 3300.
Transcript of Mathematics 1201 Unit 2: Powers and Roots
Mathematics 1201 Unit 2: Powers and Roots
3.1: Factors and Multiples of Whole Numbers Prime Factorization: the number written as a product of its prime factors Greatest Common Factor: the GCF of two or more numbers is the greatest factor the numbers have in common. Least Common Multiple: the LCM of two or more numbers is the least number that is divisible by each number. EXAMPLE: Write the prime factorization of 3300.
EXAMPLE: Determine the greatest common factor of 138 and 198. EXAMPLE: Determine the least common multiple of 18, 20, and 30.
EXAMPLE: a) What is the side length of the smallest square that could be tiled with rectangles that measure 16 cm by 40 cm? b) What is the side length of the largest square that could be used to tile a rectangle that measures 16 cm by 40 cm?
3.2: Perfect Squares, Perfect Cubes, and their Roots EXAMPLE: Determine the square root of 1296. EXAMPLE: Determine the cube root of 1728.
EXAMPLE: A cube has volume 4913 cubic inches. What is the surface area of the cube?
4.1: Estimating Roots
p. 204 worksheet will cover the outcomes for this section.
4.2: Irrational Numbers
EXAMPLE: Tell whether each number is rational or irrational. Explain how you know. a)
b) c)
EXAMPLE: Use a number line to order these numbers from least to greatest.
4.3: Mixed and Entire Radicals
EXAMPLE: Simplify each radical using prime factorization. a)
b) c)
EXAMPLE: Write each radical in simplest form, if possible. a)
b) c)
EXAMPLE: Write each mixed radical as an entire radical. a)
b) c)
4.4: Fractional Exponents and Radicals
EXAMPLE: Evaluate each power without using a calculator. a)
b) c) d)
EXAMPLE:
EXAMPLE: Evaluate:
a)
b)
c)
d)
EXAMPLE:
4.5: Negative Exponents and Reciprocals
EXAMPLE: Evaluate each power.
a)
b) c)
EXAMPLE: Evaluate each power without using a calculator.
a)
b)
EXAMPLE:
4.6: Applying the Exponent Laws
Exponent Law Handout EXAMPLE: Simplify by writing as a single power.
a)
b)
c)
d)
EXAMPLE: Simplify: a)
b)
EXAMPLE: Simplify.
a)
b)
c)
EXAMPLE: A sphere has volume 425 m3. What is the radius of the sphere to the nearest tenth of a metre?
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