Curriculum Outcomes
Algebra and Number: 1. Demonstrate an understanding of factors of whole numbers by determining the:
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Things You Need to Know
Sample Problems
- Perfect squares are where you times a number by itself and it makes a new number. That new number is a perfect square.
- Square roots are that number that you times by itself.
- Perfect cubes are similar to perfect squares, except with 3 numbers.
- Cube roots are that number that you times by itself 3 times.
- Example: 5 x 5 = 25. (25 is the perfect square. 5 is the square root.)
- Example: 2 x 2 x 2 = 8. (8 is the perfect cube. 2 is the cube root.)
- We can use prime factorization to break a number down into its prime number factors. This can tell us the square/cube root if we group the numbers.
- A number (x) with a negative exponent is equal to its reciprocal (1/x) with the positive exponent.
- If the negative exponent is in the numerator, move the number to the denominator.
- If the negative exponent is in the denominator, move the number to the numerator.
- Leave any non-negative exponents where they are.
- The Exponent Laws (page 164) help us simplify expressions involving exponents.
- Rational numbers are numbers that can written as a fraction with integers as the numerator/denominator.
- Numbers with rational exponents follow the same rules as numbers with integer exponents.
- Adding/subtracting fractions requires you to make sure both fractions have the same denominator.
- Multiplying fractions is simpler: just multiply the numerators by numerators, and denominators by denominators.
- Radicals are numbers with a root sign, an index, and a radicand.
- Index: the small number to the left of the root sign indication what order the root is (3rd root, 4th root, etc.)
- If no index is given, then the index is assumed to be 2 (2nd root, aka the square root).
- Radicand: the whole number underneath the root sign.
- Radicals can be written as numbers with rational (fraction) exponents.
- The radicand becomes the base. The exponent of the radicand under the root sign becomes the numerator (if none given, it is 1). The index of the radical becomes the denominator.
- The radicand becomes the base. The exponent of the radicand under the root sign becomes the numerator (if none given, it is 1). The index of the radical becomes the denominator.
- Numbers with rational (fraction) exponents can be written as radicals.
- Again, the base becomes the radicand. The numerator becomes the exponent of the radicand. The denominator becomes the index of the radical.
- Again, the base becomes the radicand. The numerator becomes the exponent of the radicand. The denominator becomes the index of the radical.
- Entire radicals are expressions where everything is contained under one root sign.
- Mixed radicals are expressions with a number multiplied by a radical.
- You can convert a mixed radical to an entire by taking the whole number outside the radical, taking it to the power of the radical's index, and then multiplying it by the radicand underneath the root sign.
- You can convert an entire radical to a mixed by finding the largest perfect square/cube/index that is a factor of the radicand, taking the index root of it, and then putting that answer outside the root sign.
Sample Problems
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Interactive Activities