MathEquivalent ExpressionsMedium frequency
SAT Math: Simplify radical expressions and convert between radical and exponent form
22+ practice questions in Praczo
What you need to know
The concept, explained
- 1
√(ab) = √a · √b. Use this to pull perfect squares out: √50 = √(25 · 2) = 5√2.
- 2
Convert radicals to fractional exponents: √x = x^(1/2), ∛x = x^(1/3), x^(m/n) = ⁿ√(xᵐ).
- 3
When simplifying √(xⁿ), if n is even use x^(n/2); if odd, factor one x out: √(x⁵) = x²√x.
- 4
Rationalize denominators when needed: 1/√3 = √3/3. Multiply numerator and denominator by √3.
Common mistakes
- ✗ Writing √(a + b) as √a + √b — this is WRONG. Radicals distribute over multiplication, not addition.
- ✗ Forgetting that √x² = |x|, not x, when x could be negative (usually not tested, but worth knowing).
Try a sample question
SAT-style practice
Which expression is equivalent to √72?
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