How do you rationalize the denominator and simplify 4/(6-sqrt5)46−√5?

1 Answer
Don't Memorise
Mar 27, 2016

= (24 + 4 sqrt5)/ (31)=24+4√531

Explanation:

4 / ( 6 -sqrt5)46−√5

To rationalize the denominator, we multiply the expression , by the conjugate of the denominator.

Conjugate , of 6 -sqrt5 = color(blue)( 6 + sqrt56−√5=6+√5

4 / ( 6 -sqrt5) = (4 * (color(blue)( 6 + sqrt5))) / (( 6 -sqrt5) * color(blue)( 6 + sqrt5)46−√5=4⋅(6+√5)(6−√5)⋅6+√5

  • Applying below mentioned property to simplify denominator:
    color(blue)((a-b)(a+b) = a^2 - b^2(a−b)(a+b)=a2−b2

= (4 * (color(blue)( 6)) + 4 * (sqrt5))/ (( 6 ) ^2 -(sqrt5)^2)=4⋅(6)+4⋅(√5)(6)2−(√5)2

= (24 + 4 sqrt5)/ ((36 - 5)=24+4√5(36−5)

= (24 + 4 sqrt5)/ (31)=24+4√531

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