Rationalize the denominator of the following expression 2√5-3-√5
To rationalize the denominator of the expression 2√5 - 3 - √5, we need to eliminate the square root from the denominator.
To do this, we will multiply the entire expression by the conjugate of the denominator, which is 2√5 + 3 + √5.
(2√5 - 3 - √5) * (2√5 + 3 + √5) / (2√5 + 3 + √5)
Expanding the numerator, we get:
= (2√5)(2√5) + (2√5)(3) + (2√5)(√5) + (-3)(2√5) + (-3)(3) + (-3)(√5) + (√5)(2√5) + (√5)(3) + (√5)(√5)
= 4(5) + 6√5 + 2(5) - 6√5 - 9 - 3√5 + 2(5) + 3√5 + 5
= 20 + 10 - 9 + 5
= 26
Therefore, the rationalized expression is:
26 / (2√5 + 3 + √5)