1)Identify the conjugate for 6 – 7√3 and explain your reasoning. 2)Multiply the radical expression 6 – 7√3 and its conjugate and write in simplified form. Show all your steps
3) Explain why we always get an integer when multiplying a radical expression by its conjugate? Provide your own appropriate example with supporting work that matches your explanation..

1) The conjugate for is .

2) -111

3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.

Step-by-step explanation:

1) A radical number of the form , , where the first component is a non-radical real number which acts as a "pivot" and the second component is the radical component, which generates a "displacement" from pivot.

The conjugate of is a real number ,  , which that is "pivot" plus "displacement" in the direction opposite to that of . We proceed to complement this explanation with the image attached below.

Then, the conjugate for is .

2) We proceed to performed all the need algebraic operation until result is found:

1) Given

2) Distributive property

3) Definition of subtraction/

4) Distributive, associative and commutative properties

5) Definition of multiplication//Definition of square root

6) Commutative, associative and distributive properties/

7) Definition of subtraction/Existence of additive inverse

8)

9) Modulative property/Result

3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.

to have more of what you want like money

step-by-step explanation:

save it by not spending on unnecessary stuff and have more