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Rationalize the denominator. simplify your answer. 5+sqrt3/2-sqrt3

Rationalize the denominator. simplify your answer. 5+sqrt3/2-sqrt3-example-1
User AbbeGijly
by
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1 Answer

2 votes

Answer:


13 + 7√(3)

Explanation:

Given


(5 + √(3))/(2 - √(3))

Required

Rationalize

To rationalize, we have to multiply the numerator and the denominator by
{2 + √(3)}

This gives


(5 + √(3))/(2 - √(3)) * (2 + √(3))/(2 + √(3))


((5 + √(3))(2 + √(3)))/((2 - √(3))(2 + √(3)))

Expand


(5(2 + √(3))+√(3)(2 + √(3)))/(2(2 + √(3)) - √(3)(2 + √(3)))

Open the brackets


(10 + 5√(3)+2√(3) + (√(3))^2)/(4 + 2√(3) - 2√(3) - (√(3))^2)


(10 + 5√(3)+2√(3) + 3)/(4 + 2√(3) - 2√(3) - 3)

Collect like terms for ease of arithmetic operations


(10 + 3 + 5√(3)+2√(3))/(4 -3 + 2√(3) - 2√(3))


(13 + 7√(3))/(1 )


13 + 7√(3)

Hence,


(5 + √(3))/(2 - √(3)) is equivalent to
13 + 7√(3), after rationalizing the denominator

User Tech Learner
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