Question

a) combine the expressions
$3\sqrt{x} + 5.9\sqrt{x} - 2.1\sqrt{x}$
answer:

b) combine the expressions
$-3.1\sqrt{x} + 2\sqrt{x} + 3.4\sqrt{x}$
answer:

5)
what is the value of $\frac{\sqrt{45x^4}}{3\sqrt{4x^4}}$ for all real numbers $x$, where $x \
eq 0$?
answer:

6)
simplify the radical $\sqrt{24m^6n^7}$.
answer:

7)
what is the equation of the function $f(x)$ obtained by reflecting the graph of $f(x) = \sqrt{x + 6}$ vertically?
answer:

8)
a) write $\sqrt4{x^9}$ in exponential form.
answer:

b) write $\sqrt8{x^{11}}$ in exponential form.
answer:

9)

Explanation:

5a)

Step1: Identify like terms

All terms have \(\sqrt{x}\), so they are like terms.

Step2: Combine coefficients

Add/subtract coefficients: \(3 + 5.9 - 2.1 = 6.8\)

Step3: Write combined term

Multiply by \(\sqrt{x}\): \(6.8\sqrt{x}\)

Step1: Identify like terms

All terms have \(\sqrt{x}\), so they are like terms.

Step2: Combine coefficients

Add/subtract coefficients: \(-3.1 + 2 + 3.4 = 2.3\)

Step3: Write combined term

Multiply by \(\sqrt{x}\): \(2.3\sqrt{x}\)

Step1: Simplify numerator radical

\(\sqrt{45x^4} = \sqrt{9 \cdot 5 \cdot x^4} = 3x^2\sqrt{5}\) (since \(x
eq 0\), \(x^2\) is positive)

Step2: Simplify denominator radical

\(3\sqrt{4x^4} = 3 \cdot 2x^2 = 6x^2\)

Step3: Divide numerator by denominator

\(\frac{3x^2\sqrt{5}}{6x^2} = \frac{\sqrt{5}}{2}\) (cancel \(x^2\) as \(x
eq 0\))

Answer:

\(6.8\sqrt{x}\)

5b)