Exponents and radicals
Adding and subtracting radicals worksheets
Choose already simplified radicals, simplify-one, simplify-all or mixed problems for 10 sums and differences. Select unit, nonunit or mixed coefficients.
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Simplifying radical expressions worksheets
Practice 10 numeric-only, variable-only or mixed radicals with square, cube, fourth, fifth or sixth roots. Extract perfect powers and use absolute values where even roots require them.
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Extract perfect powers matching the root index. Read the printed domain and include absolute values when simplifying even roots of variable powers.
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Read the domain before removing the radical
Variables are real, with any extra radicand conditions printed on the task. An even root returns a nonnegative value, so √(x²) is |x|. An odd root preserves sign, so ∛(x³) is x.
Test a proposed simplification at a negative value that satisfies the original domain. This often reveals a missing absolute value.
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Learning objective
What this activity builds
Simplify indexed radicals over their stated real domains and distinguish even-root absolute values from odd-root signs.
Worked example
Simplify the fourth root of 81x⁴ for real x.
3|x|.
81 is 3⁴. The principal fourth root is nonnegative, so the fourth root of x⁴ is |x|, including when x is negative.
Teaching notes
Make the practice count
- Read the root index before factoring.
- Group variable exponents into multiples of that index.
- Try a negative substitution to check an even-root answer.
- Compare a cube root of x³ with a square root of x².
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