Question 1Easier
?
Show answer
Answer: C — 30
and , so the product is .
Study on the flyACTMathematicsRadicals and roots
Radicals and roots — ACT practice questions
- Mathematics
- 45 questions on the paper
- 36 practice questions in the app
- Free
Practice 36 Radicals and roots questions in the app
What this topic is
Radicals and roots on the ACT Mathematics test covers products of square roots, conjugate pairs, and binomials that mix integers with roots.
A student has to multiply radicals, apply the difference of squares to a conjugate, expand a squared two-term radical expression, and then simplify until the result is an integer or a fully reduced radical. Items are usually a compact expression set equal to a question mark, with five answer choices that mix integers and leftover roots.
Common traps include dropping the middle term when squaring, keeping an unsimplified radical, or flipping a sign on a conjugate.
Sample questions
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 2Easier
?
Show answer
Answer: C — 5
The factors are conjugates, so their product is the difference of squares: .
Question 3Mid
?
Show answer
Answer: A —
Using gives .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
Study on the fly is an independent study tool and is not affiliated with, sponsored by, or endorsed by any testing organization, school, or government body.
ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, and does not endorse, this product.
All practice questions and passages are original works created for Study on the fly and are not reproduced from any official test.