Simplify the radical expression

Question

(5+√3)(5-√3)

Answer 1

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.

Answer 2

Choices are
A.16
B.22
C.25+10√3
D.16+10√3

Answer 3

The correct answer is B.

(5+√3)(5-√3) = 5² - (√3)² = 25 - 3 = 22

Therefore, the answer is B.

Answer 4

Y=√4x+8

Answer 5

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.

Answer 6

√8/√6x

Answer 7

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.