Simplify the radical expression
(5+√3)(5-√3)
This is an example of the difference of squares pattern:
(5+√3)(5-√3) = 5² - (√3)²
Simplifying:
= 25 - 3
= 22
Therefore, (5+√3)(5-√3) simplified is 22.
Choices are
A.16
B.22
C.25+10√3
D.16+10√3
The correct answer is B.
(5+√3)(5-√3) = 5² - (√3)² = 25 - 3 = 22
Therefore, the answer is B.
Y=√4x+8
This is a square root function where the input is 4x+8 and the output is the square root of that expression.
To graph this function, we can start by making a table of values.
|x| y = √4x+8|
|---|---|
|0|2|
|1|2.449|
|2|2.828|
|3|3.162|
|4|3.464|
We can plot these points on a coordinate plane and connect them with a smooth curve.
Note that the domain of this function is all real numbers greater than or equal to -2. The range is all real numbers greater than or equal to 0. Additionally, the function is always increasing and never touches the x-axis.
√8/√6x
To simplify this expression, we can use the fact that √(ab) = √a * √b.
So,
√8/√6x = √(8/6) * √(1/x) = √(4/3) * √(1/x)
We can simplify √(4/3) as follows:
√(4/3) = √(4/3) * √(3/3)
= √(12/9)
= √4 * √(3/9)
= 2 * (√3/3)
Putting it all together, we get:
√8/√6x = 2 * (√3/3) * √(1/x)
= 2√(3/x) / 3
Therefore, √8/√6x simplified is 2√(3/x) / 3.