Download Part 1-3 Combined Handout

Math 10c – Unit 1 Factors, Powers and Radicals – Key Concepts
1.1 Determine the prime factors of a whole number.
Ex.
650
Ex.
3910
1.2 Explain why the numbers 0 and 1 have no prime factors.
1.3 Determine, using a variety of strategies, the greatest common factor or least common multiple of
a set of whole numbers, and explain the process.
Ex. Find the GCF (answer is a smaller # than your original #s)
48
204
Ex. Find the LCM (answer is a bigger # than your original #s)
4
27
32
1.4 Determine, concretely, whether a given whole number is a perfect square, a perfect cube or
neither.
1.5 Determine, using a variety of strategies, the square root of a perfect square, and explain the
process. (Hint: USE PRIME FACTORIZATION)
1.6 Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process.
(Hint: USE PRIME FACTORIZATION)
Ex.
625
Ex.
444
Ex.
64
1.7 Solve problems that involve prime factors, greatest common factors, least common multiples,
square roots or cube roots
Ex. A farmer has a rectangular plot of land measuring 400 m by 640 m. He wants to subdivide this land
into congruent square pieces. What is the side length of the largest possible square?
Ex. What are the dimensions of the smallest square that could be tiled using 18-cm by 24-cm tile?
Assume the tiles cannot be cut.
2.1 Sort a set of numbers into rational and irrational numbers.
Ex. Identify as Rational or Irrational
7
a) − 5
b) 0.234234234…
c) √144
d) 0.23223222322223222223…
2.2 Determine an approximate value of a given irrational number. (Estimate without calculator)
a) √17
b) √20
c) √105
2.3 Approximate the locations of irrational numbers on a number line, using a variety of strategies, and explain
the reasoning.
2.4 Order a set of irrational numbers on a number line.
a) √15
b) 2√7
c) √0.8
d) √60
e) √310
f) 𝜋
2.5 Express a radical as a mixed radical in simplest form (limited to numerical radicands).
5
a) − 6 √304
b) √980
c) 4√272
d) −3√288
2.6 Express a mixed radical as an entire radical (limited to numerical radicands)
53
3
4
a) 6 √108
b) 5 √162
c) −5√52
d) −2√625
2.7 Explain, using examples, the meaning of the index of a radical.
Ex. 3√48𝑦
2.8 Represent, using a graphic organizer, the relationship among the subsets of the real numbers (natural, whole,
integer, rational, irrational).
3.1 Explain, using patterns, why a-n= 1/an, a≠0 /
3.2 Explain, using patterns, why a1/n = n√𝒂, n>0
Ex.
Ex.
103 =
102 =
101 =
100 =
10-1 =
10-2 =
3.3 Apply the exponent laws to expressions with rational and variable bases and integral and rational exponents,
and explain the reasoning:

(am)(an) = am+n

am ÷ an = am-n, a≠0

(am)n = amn
1. (43 )5

(ab)m = ambm
1. (𝑐𝑑)4

(a/b)n = an/bn, b≠0
4𝑥 2 ∙ 3𝑥 7
1.
1.
𝒚𝟐
1. (𝒛𝟑 )𝟑
2. 𝑦 −1 ∙ 𝑦 ∙ 𝑦 4
24𝑦12 ÷ 3𝑦 3
2. (3𝑐 −1 𝑑2 )4
𝑥 3 𝑦 2 𝑧 −2
2. 𝑥 −1 𝑦2 𝑧4
3. 8−3 ∙ 82 ∙ 8−4 ∙ 87
3.4 Express powers with rational exponents as radicals and vice versa.
4
3
3
Ex. 63 = √64 or (√6)4
Ex. √57 =
3.5 Solve a problem that involves exponent laws or radicals.
Ex. A square has an area of 1134 m2. Determine the perimeter of the square. Write the answer as a radical in
simplest form.
3.6 Identify and correct errors in a simplification of an expression that involves powers
Ex.