Solve \(\frac{4x 2\sqrt{x}}{\sqrt{18x}}\)

Question

\frac{4 x \times 2 x}{18 x}

Simplify the expression

\frac{4 2 \times x}{3}

Evaluate

\frac{4 x \times 2 x}{18 x}

Simplify the root

More Steps

Evaluate

18 x

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 2 x

Write the number in exponential form with the base of 3

3^{2} \times 2 x

The root of a product is equal to the product of the roots of each factor

3^{2} \times 2 x

Reduce the index of the radical and exponent with 2

3 2 x

\frac{4 x \times 2 x}{3 2 x}

Multiply the terms

\frac{8 x x}{3 2 x}

Factor the expression

\frac{8 x x}{3 2 \times x}

Reduce the fraction

\frac{8 x}{3 2}

Multiply by the Conjugate

\frac{8 x 2}{3 2 \times 2}

Calculate

\frac{8 x 2}{3 \times 2}

Calculate

\frac{8 2 \times x}{3 \times 2}

Calculate

\frac{8 2 \times x}{6}

Solution

\frac{4 2 \times x}{3}

Show Solution

x \in \emptyset

Evaluate

(\frac{4 x \times 2 x}{18 x})

To find the roots of the expression,set the expression equal to 0

\frac{4 x \times 2 x}{18 x} = 0

Find the domain

More Steps

Evaluate

⎩ ⎨ ⎧ x \geq 0 18 x \geq 0 18 x \neq = 0

Calculate

⎩ ⎨ ⎧ x \geq 0 x \geq 0 18 x \neq = 0

Calculate

More Steps

Evaluate

18 x \neq = 0

Calculate

18 x \neq = 0

Rewrite the expression

x \neq = 0

⎩ ⎨ ⎧ x \geq 0 x \geq 0 x \neq = 0

Simplify

{x \geq 0 x \neq = 0

Find the intersection

x > 0

\frac{4 x \times 2 x}{18 x} = 0, x > 0

Calculate

\frac{4 x \times 2 x}{18 x} = 0

Simplify the root

More Steps

Evaluate

18 x

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 2 x

Write the number in exponential form with the base of 3

3^{2} \times 2 x

The root of a product is equal to the product of the roots of each factor

3^{2} \times 2 x

Reduce the index of the radical and exponent with 2

3 2 x

\frac{4 x \times 2 x}{3 2 x} = 0

Multiply the terms

\frac{8 x x}{3 2 x} = 0

Divide the terms

More Steps

Evaluate

\frac{8 x x}{3 2 x}

Factor the expression

\frac{8 x x}{3 2 \times x}

Reduce the fraction

\frac{8 x}{3 2}

\frac{8 x}{3 2} = 0

Simplify

8 x = 0

Rewrite the expression

x = 0

Check if the solution is in the defined range

x = 0, x > 0

Solution

x \in \emptyset

Show Solution