Solve 3x * x^(1/2)

Question

Simplify the expression

3 x x

Evaluate

3 x \times x^{\frac{1}{2}}

Multiply the terms with the same base by adding their exponents

3 x^{1 + \frac{1}{2}}

Add the numbers

More Steps

Evaluate

1 + \frac{1}{2}

Reduce fractions to a common denominator

\frac{2}{2} + \frac{1}{2}

Write all numerators above the common denominator

\frac{2 + 1}{2}

Add the numbers

\frac{3}{2}

3 x^{\frac{3}{2}}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

3 x^{3}

Solution

More Steps

Evaluate

x^{3}

Rewrite the exponent as a sum

x^{2 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

x^{2} \times x

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

x^{2} \times x

Reduce the index of the radical and exponent with 2

x x

3 x x

Show Solution

x = 0

Evaluate

3 x \times x^{\frac{1}{2}}

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

3 x \times x^{\frac{1}{2}} = 0

Find the domain

3 x \times x^{\frac{1}{2}} = 0, x \geq 0

Calculate

3 x \times x^{\frac{1}{2}} = 0

Multiply

More Steps

Multiply the terms

3 x \times x^{\frac{1}{2}}

Multiply the terms with the same base by adding their exponents

3 x^{1 + \frac{1}{2}}

Add the numbers

More Steps

Evaluate

1 + \frac{1}{2}

Reduce fractions to a common denominator

\frac{2}{2} + \frac{1}{2}

Write all numerators above the common denominator

\frac{2 + 1}{2}

Add the numbers

\frac{3}{2}

3 x^{\frac{3}{2}}

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

Rewrite the expression

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

The only way a root could be 0 is when the radicand equals 0

x = 0

Check if the solution is in the defined range

x = 0, x \geq 0

Solution

x = 0

Show Solution