Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Rationalize the denominator. \newline6−6−3\frac{6}{-6 - \sqrt{3}}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Simplify radical expressions using conjugatesright chevron icon

Full solution

Q. Simplify. Rationalize the denominator. \newline6−6−3\frac{6}{-6 - \sqrt{3}}
  1. Identify Conjugate: Identify the conjugate of the denominator.\newlineThe conjugate of a−ba - \sqrt{b} is a+ba + \sqrt{b}. Therefore, the conjugate of −6−3-6 - \sqrt{3} is −6+3-6 + \sqrt{3}.
  2. Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator.\newlineTo rationalize the denominator, we multiply the expression by a fraction equivalent to 11 that has the conjugate of the denominator as both its numerator and denominator.\newline6−6−3\frac{6}{-6 - \sqrt{3}} * −6+3−6+3\frac{-6 + \sqrt{3}}{-6 + \sqrt{3}}
  3. Apply Distributive Property: Apply the distributive property to multiply the numerators and the denominators.\newlineNumerator: 6×(−6+3)=−36+6×36 \times (-6 + \sqrt{3}) = -36 + 6\times\sqrt{3}\newlineDenominator: (−6−3)×(−6+3)=(−6)2−(3)2=36−3(-6 - \sqrt{3}) \times (-6 + \sqrt{3}) = (-6)^2 - (\sqrt{3})^2 = 36 - 3
  4. Simplify Numerator and Denominator: Simplify the expressions obtained in the numerator and the denominator.\newlineNumerator: −36+63-36 + 6\sqrt{3}\newlineDenominator: 36−3=3336 - 3 = 33\newlineSo the expression becomes −36+6333\frac{-36 + 6\sqrt{3}}{33}
  5. Simplify Fraction: Simplify the fraction by dividing both the terms in the numerator by the denominator.\newline−3633+6333-\frac{36}{33} + \frac{6\sqrt{3}}{33}\newline= −1211+2311-\frac{12}{11} + \frac{2\sqrt{3}}{11}

More problems from Simplify radical expressions using conjugates

Question
Simplify. \newline925\sqrt{\frac{9}{25}}\newline_____________
Get tutor helpright-arrow

Posted 2 months ago

Question
Convert.\newline1,0001,000 milligrams\text{ milligrams}=____\_\_\_\_ grams\text{ grams}
Get tutor helpright-arrow

Posted 2 months ago

Question
A 33-gallon bottle of bleach costs $11.52\$11.52. What is the price per quart?\newline`$`_____
Get tutor helpright-arrow

Posted 2 months ago

Question
Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for 88 ounces of chocolate chips per loaf. If she has enough zucchini to make 44 loaves of zucchini bread, how many pounds of chocolate chips does she need?\newlineHint: There are 1616 ounces in 11 pound.\newlineWrite your answer as a whole number, decimal, or simplified fraction. Do not round.\newline____ pounds
Get tutor helpright-arrow

Posted 2 months ago

Question
A whale is swimming due north at a speed of 3030 miles per hour. Just 55 miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 4646 miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute. ____\_\_\_\_ hours and ____\_\_\_\_ minutes
Get tutor helpright-arrow

Posted 2 months ago

Question
Convert. \newline 500500 milligrams == _____ grams
Get tutor helpright-arrow

Posted 3 months ago

Question
Convert. \newline 2,0002,000 milligrams == _____ grams
Get tutor helpright-arrow

Posted 3 months ago

Question
Convert. \newline 750750 milligrams == _____ grams
Get tutor helpright-arrow

Posted 3 months ago

Question
Convert. \newline1,5001,500 milligrams == _____ grams
Get tutor helpright-arrow

Posted 3 months ago

Question
Convert. \newline1,5001,500 milligrams == _____ grams
Get tutor helpright-arrow

Posted 3 months ago

View all (29)