Solve sqrt(x x^2)

Question

Simplify the expression

x x

Evaluate

x \times x^{2}

Multiply the terms

More Steps

Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

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

Solution

x x

Show Solution

x = 0

Evaluate

x \times x^{2}

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

x \times x^{2} = 0

Find the domain

More Steps

Evaluate

x \times x^{2} \geq 0

Multiply the terms

More Steps

Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

x^{3} \geq 0

The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0

x \geq 0

x \times x^{2} = 0, x \geq 0

Calculate

x \times x^{2} = 0

Multiply the terms

More Steps

Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

x^{3} = 0

Simplify the root

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

x x = 0

Separate the equation into 2 possible cases

x = 0 x = 0

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

x = 0 x = 0

Find the union

x = 0

Check if the solution is in the defined range

x = 0, x \geq 0

Solution

x = 0

Show Solution