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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

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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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