Question

Simplify the following expression by multiplying by the conjugate: fraction numerator 6 plus 10 square root of 3 over denominator square root of 3 minus 1 end fraction a.) 18 plus 8 square root of 3 b.) 24 plus 6 square root of 3 c.) 1 plus 10 square root of 3 d.) 3 plus 5 square root of 3

Answer 1

To simplify the given expression, multiply the numerator and denominator by the conjugate of the denominator. Simplifying the expression gives 3 + 8√3.

Step-by-step explanation:

To simplify the given expression using the conjugate, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √3 - 1 is √3 + 1.

So, the simplified expression is:

(6 + 10√3)(√3 + 1) / (√3 - 1)(√3 + 1)

Expanding the expression and simplifying, we get:

(6√3 + 6 + 10√9 + 10) / (3 - 1)

Simplifying further, we have:

(6 + 16√3) / 2

Which simplifies to:

3 + 8√3