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, ∞)
simplify the rational expression by rationalizing the denominator.
sqrt12/sqrt8x
To simplify this rational expression, we can start by rationalizing the denominator (i.e., simplifying the denominator so that it contains no radical symbols). To do this, we can multiply both the numerator and the denominator by the same expression that will eliminate the radical in the denominator. Here, we can multiply the numerator and denominator by sqrt(2), because:
sqrt(8x) = sqrt(4 x 2 x x) = 2sqrt(2x)
So we have:
sqrt(12) / sqrt(8x) = (sqrt(12) / sqrt(8x)) x (sqrt(2) / sqrt(2))
= (sqrt(12 x 2) / sqrt(8x x 2))
= (sqrt(24) / sqrt(16x))
= (sqrt(4 x 6) / (4sqrt(x)))
= (2 sqrt(6)) / (4sqrt(x))
= sqrt(6) / (2sqrt(x))
= sqrt(6 / (2x))
Therefore, the simplified expression is sqrt(6 / (2x)).
simplify 4sqrt6/sqrt30 by rationalizing the denominator
To simplify this expression, we can start by rationalizing the denominator (i.e., simplifying the denominator so that it contains no radical symbols). To do this, we can multiply both the numerator and the denominator by the same expression that will eliminate the radical in the denominator. Here, we can multiply the numerator and denominator by sqrt(30), because:
sqrt(30) = sqrt(6 x 5)
So we have:
(4sqrt(6)) / sqrt(30) = (4sqrt(6)) / (sqrt(6) x sqrt(5))
= (4sqrt(6)) / sqrt(6) / sqrt(5))
= (4sqrt(6) / sqrt(6)) x (1 / sqrt(5))
= (4 x sqrt(6 x 6)) / (6 x sqrt(5))
= (4 x 6) / (6 x sqrt(5))
= 24 / (6sqrt(5))
= (24 / 6) x (1 / sqrt(5))
= 4 / sqrt(5)
Therefore, the simplified expression is 4/sqrt(5).