Products and Quotients of Radicals
Products and quotients of radicals is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students simplify expressions involving multiplication and division of radicals. The product rule states sqrt(a) times sqrt(b) = sqrt(ab), and the quotient rule states sqrt(a)/sqrt(b) = sqrt(a/b).
Key Concepts
Property We can multiply or divide radicals that have the same index, even if their radicands are different. The Product and Quotient Rules are used to combine the expressions under a single radical.
Product Rule: $$\sqrt{a}\sqrt{b} = \sqrt{ab} \quad (a, b \geq 0)$$.
Quotient Rule: $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \quad (a \geq 0, b 0)$$.
Common Questions
What is the product rule for radicals?
The nth root of a times the nth root of b equals the nth root of ab: sqrt(a) * sqrt(b) = sqrt(ab).
How do you simplify sqrt(3) * sqrt(12)?
sqrt(3) * sqrt(12) = sqrt(36) = 6.
What is the quotient rule for radicals?
sqrt(a)/sqrt(b) = sqrt(a/b), for b > 0.
How do you simplify sqrt(50)/sqrt(2)?
sqrt(50)/sqrt(2) = sqrt(50/2) = sqrt(25) = 5.