User:
• Matrices
• Algebra
• Geometry
• Funciones
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

Simplify radical expressions by rationalizing the denominator

# Simplify radical expressions by rationalizing the denominator

To simplify radical expressions by rationalizing the denominator it will be useful to remember the following properties.

• The multiplication property of square roots states that

$sqrt{ab}=\;sqrt{a}sqrt{b}$

• The division property of square roots states that

$sqrt{\frac{a}{b}}=\;\frac{sqrt{a}}{sqrt{b}}$

Simplify $sqrt{\frac{5}{3}}$

To simplify this radical expression, rewrite it with a radical in the numerator and a radical in the denominator. Then factor out any perfect squares and simplify.

$sqrt{\frac{5}{3}}$
=$sqrt{\frac{5}{3}}$   Find the prime factorizations of the numerator and denominator
=$\frac{sqrt{5}}{sqrt{3}}$   Apply the division property of square roots

To finish simplifying the expression, multiply by $\frac{sqrt{3}}{sqrt{3}}$ to rationalize the denominator.

$\frac{sqrt{5}}{sqrt{3}}\;\cdot\;\frac{sqrt{3}}{sqrt{3}}$

=$\frac{sqrt{5\cdot3}}{(sqrt{3})^2}$

Simplify
=$\frac{sqrt{5\cdot3}}{3}$

Simplify the denominator
=$\frac{sqrt{15}}{3}$   Multiply

Simplify.

$\sqrt{\frac{7}{1}$

$\frac{Array}{\sqrt{}}Solution\;=$