# RATIONALIZING DENOMINATORS

can you please show me how to solve this equation step by step because I am definitely doing something wrong:

4 x square root 15 / 4 x square root 80

### Comments for RATIONALIZING DENOMINATORS

 Sep 07, 2011 Simplify Radical Expression by: Staff The question: can you please show me how to solve this equation step by step because I am definitely doing something wrong: 4 x square root 15 / 4 x square root 80 The answer: 4 x square root 15 / 4 x square root 80 [4*√(15)]/[4*√(80)] Simplifying this expression automatically eliminates the denominator. [4*√(15)]/[4*√(80)] As you can see, the number 4 appears in both the numerator and denominator. [4*xxxxxxxx]/[4*xxxxxxxx] You can cancel the 4’s = [√(15)/√(80)]*(4/4) = [√(15)/√(80)]*(1) = [√(15)/√(80)] Factor the numbers under the radical signs = √(3*5)/√(5*4*4) = √(3*5)/√(5*4²) Simplify the denominator = √(3*5)/√(5*4²) = √(3*5)/[4√(5)] Break the expression into two fractions = (1/4)*[√(3*5)/√(5)] Using the distributive law for radicals, combine the two radical expressions under a single radical sign = (1/4)*[√(3*5/5)] The 5’s cancel = (1/4)*{√[3*(5/5)]} = (1/4)*{√[3*(1)]} = (1/4)*[√(3)] Multiply the two fractions = (1/4)*[√(3)/1] = [1*√(3)]/(4*1) = [1*√(3)]/(4*1) = [√(3)]/(4*1) = [√(3)]/4 The final answer is: [√(3)]/4, the √(3) divided by 4. Check this answer against the original expression with a calculator: Final answer: [√(3)]/4 = 0.433013 Original expression: [4*√(15)]/[4*√(80)] = 0.433013 Since [√(3)]/4 and [4*√(15)]/[4*√(80)] are equivalent numerically, the final answer of [√(3)]/4 is valid. Thanks for writing. Staff www.solving-math-problems.com

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