Real Numbers: Operations and Exponents

Name: Real Numbers: Operations and Exponents
Author: StemPy Lab

What happens when you add or multiply an irrational number? How do you remove a square root from the bottom of a fraction? Here we learn the rules, we rationalise denominators, and we use the laws of exponents with fractional powers.

3 lessons, about 1 h 15 min3 simulations10 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Operations on real numbers
Rational numbers stay rational under the four operations. A rational plus an irrational number is irrational, and so is a non-zero rational times an irrational. Two irrational numbers can give either kind. Roots multiply and divide neatly, but they do not add that way. Four identities help to simplify.
1 simulation2 practice questions1 Python program4 problems
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Lesson 2about 25 min
Rationalising the denominator
Rationalising removes the square root from a denominator by multiplying the top and bottom by the same number, which does not change the value. For one square root, one over root a becomes root a over a. For a denominator such as a plus root b, multiply by the conjugate a minus root b, and the product is a squared minus b, with no root. The conjugate of root a minus root b is root a plus root b. We can check the answer with decimal values, and rationalising helps to simplify sums and to find values with a calculator.
1 simulation2 practice questions1 Python program3 problems1 Python lab
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Lesson 3about 25 min
Laws of exponents
The laws of exponents: multiply by adding the powers, raise a power by multiplying them, and divide by taking them away. Any base to the power 0 is 1, and a negative power means a reciprocal. A fractional power a to the 1 over n is the n-th root of a, and a to the m over n is that root to the power m. Take the root first.
1 simulation2 practice questions1 Python program3 problems1 Python lab1 question set1 note
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Radicals and Exponents: Challenge Paper

10 questions · 20 min

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Real Numbers: Operations and Exponents

Course outline (3 lessons)

Operations on real numbers

Rationalising the denominator

Laws of exponents

Test Your Learning

Your teacher

Discussion (0)