Question

Create your own binomial expression with a radical in the second term.

Part 1: Identify its conjugate and explain, in complete sentences, why it is the conjugate. (1 point)

Part 2: Multiply your original binomial expression and its conjugate. What happened to the radicals and why? (1 point)

Answer 1

please help me

Answer 2

\[2+\sqrt{3}\]

Answer 3

The conjugate is \[2-\sqrt{3}\] because if the two are multiplied together, the radical is eliminated.

Answer 4

\[(2-\sqrt{3})(2+\sqrt{3})= 4+2\sqrt{3}-2\sqrt{3}-3 =1\]

Answer 5

The radicals were eliminated because the outer and inner terms are opposites and the last term is the square of a square root which eliminates the radical.

Answer 6

- in cases like this us always formula :

\[a ^{2}-b ^{2}=(a-b)(a+b)\]

- and hence ,on this way will be eliminated the radical

Answer 7

- so again this is exactly like in cases of complex numbers when we us the conjugate for one denominator without i