Asked by Jamie Illasarie on May 20, 2024
Verified
Multiply the expression by its conjugate and simplify. 83+48 \sqrt { 3 } + \sqrt { 4 }83+4
A) 48
B) 70
C) 188
D) 20
E) 572
Conjugate
A binomial formed by changing the sign of the second term of another binomial, commonly used to rationalize denominators.
- Acquire knowledge about the method of multiplying expressions with their conjugates and how it aids in the simplification of expressions.
Verified Answer
BP
Bruno PolonioMay 27, 2024
Final Answer :
C
Explanation :
The conjugate of 83+48 \sqrt { 3 } + \sqrt { 4 }83+4 is 83−48 \sqrt { 3 } - \sqrt { 4 }83−4 . Multiplying the expression by its conjugate, we get: (83+4)(83−4)=64⋅3−4=192−4=188.(8 \sqrt { 3 } + \sqrt { 4 })(8 \sqrt { 3 } - \sqrt { 4 }) = 64 \cdot 3 - 4 = 192 - 4 = 188.(83+4)(83−4)=64⋅3−4=192−4=188.
Learning Objectives
- Acquire knowledge about the method of multiplying expressions with their conjugates and how it aids in the simplification of expressions.