Rationalise the denominator and simplify 3 <msqrt> 2 </msqr

cazinskup3

cazinskup3

Answered question

2022-06-16

Rationalise the denominator and simplify 3 2 4 3 2 + 4
Does someone have an idea how to work 3 2 4 3 2 + 4 by rationalising the denominator method and simplifying?

Answer & Explanation

Marlee Norman

Marlee Norman

Beginner2022-06-17Added 18 answers

3 2 4 3 2 + 4 3 2 4 3 2 4 =
= 18 24 2 + 16 ( 3 2 ) 2 4 2 = 34 24 2 18 16 = 2 ( 17 12 2 ) 2 =
= 17 12 2 .
Yahir Crane

Yahir Crane

Beginner2022-06-18Added 9 answers

For problems like this, you need to multiply numerator and denominator by the denominator's conjugate. A conjugate is found by flipping the sign from positive to negative or negative to positive in a binomial. So, the denominator's conjugate in the above's equation is 3 2 4. Multiplying an irrational binomial by it's conjugate will rationalize it, as seen below:
3 2 4 3 2 + 4 × 3 2 4 3 2 4
Multiply out the bottom and top
9 × 2 12 2 12 2 + 16 9 × 2 16
= 18 24 2 + 16 18 16
= 34 24 2 2
= 17 12 2

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