simplify the radical expression
sqrt 5 +6 sqrt5
sqrt5+6sqrt5 = sqrt5(1+6) = 7sqrt5.
for any x, x + 6x = 7x
You just happen to have x = sqrt5
Uh
Oh sorry. I see what you mean. Yes, sqrt(5) + 6sqrt(5) can be simplified as:
sqrt(5) + 6sqrt(5) = (1 + 6)sqrt(5) = 7sqrt(5)
So the simplified expression is 7sqrt(5).
simplify the radical expression. 5sqrt7+2sqrt175
To simplify this expression, we can start by factoring out the largest perfect square that divides both terms inside the radical:
5sqrt(7) + 2sqrt(175) = 5sqrt(7) + 2sqrt(5 x 5 x 7)
Since 5 x 5 = 25 is a perfect square that divides 175, we can rewrite the expression as:
5sqrt(7) + 2sqrt(5 x 5 x 7) = 5sqrt(7) + 2sqrt(25 x 7)
Using the product property of radicals, we can simplify the expression as:
5sqrt(7) + 2sqrt(25 x 7) = 5sqrt(7) + 2 x 5sqrt(7)
Finally, we can combine like terms to obtain:
5sqrt(7) + 2 x 5sqrt(7) = 5sqrt(7) + 10sqrt(7) = 15sqrt(7)
Therefore, the simplified expression is 15sqrt(7).
simplify the radical expression.
(3+sqrt6)(3-sqrt6)
To simplify this expression, we can use the difference of squares formula, which states that:
(a + b)(a - b) = a^2 - b^2
In this case, a = 3 and b = sqrt(6). So, we have:
(3 + sqrt(6))(3 - sqrt(6)) = 3^2 - (sqrt(6))^2
Simplifying the right hand side, we get:
3^2 - (sqrt(6))^2 = 9 - 6 = 3
Therefore, the simplified expression is just 3.
what is the domain of the function?
y=sqrt4x+8
The expression sqrt(4x + 8) is defined only for non-negative values of the radicand (the expression inside the radical). Therefore, we must ensure that 4x + 8 is non-negative.
We can solve 4x + 8 ≥ 0 by subtracting 8 from both sides:
4x ≥ -8
Then, we can divide both sides by 4:
x ≥ -2
Therefore, the domain of the function y = sqrt(4x + 8) is all real numbers greater than or equal to -2, or in interval notation:
[-2, ∞)