What is domain of the function? y = sqaure root 3+ 3
a, x < -1
b, x > 1
c, x > -1
d, x < 1
The correct answer is b, x > 1.
To find the domain of a square root function, we need to ensure that the value inside the square root is non-negative. In this case, we have y = square root(3 + 3), so 3 + 3 = 6. Since 6 is greater than 0, the domain of this function is all real numbers greater than 1.
Simplify the rational expression by rationalizing the denominator.
sqaure root 15 sqaure root 6x
To simplify the rational expression \(\frac{\sqrt{15}\sqrt{6x}}{1}\), we want to rationalize the denominator.
First, multiply the numerator and denominator by \(\sqrt{6x}\) to rationalize the denominator:
\(\frac{\sqrt{15}\sqrt{6x}\cdot \sqrt{6x}}{1\cdot \sqrt{6x}} = \frac{\sqrt{15}\cdot 6x}{\sqrt{6x}} = \frac{6x\sqrt{15}}{\sqrt{6x}}\)
To simplify further, we can rewrite \(\sqrt{6x}\) as \(\sqrt{6}\sqrt{x}\):
\(\frac{6x\sqrt{15}}{\sqrt{6}\sqrt{x}} = \frac{6\sqrt{15}x}{\sqrt{6}\sqrt{x}} = \frac{6\sqrt{15}x}{\sqrt{6x}}\)
Therefore, the simplified expression after rationalizing the denominator is \(\frac{6\sqrt{15}x}{\sqrt{6x}}\).