Solve \sqrt{54x^7}

Question

Simplify the expression

3 x^{3} 6 x

Evaluate

54 x^{7}

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

9 \times 6 x^{7}

Write the number in exponential form with the base of 3

3^{2} \times 6 x^{7}

Rewrite the exponent as a sum

3^{2} \times 6 x^{6 + 1}

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

3^{2} \times 6 x^{6} \times x

Reorder the terms

3^{2} x^{6} \times 6 x

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

3^{2} x^{6} \times 6 x

Solution

3 x^{3} 6 x

Show Solution

x = 0

Evaluate

54 x^{7}

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

54 x^{7} = 0

Find the domain

More Steps

Evaluate

54 x^{7} \geq 0

Rewrite the expression

x^{7} \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

54 x^{7} = 0, x \geq 0

Calculate

54 x^{7} = 0

Simplify the root

More Steps

Evaluate

54 x^{7}

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

9 \times 6 x^{7}

Write the number in exponential form with the base of 3

3^{2} \times 6 x^{7}

Rewrite the exponent as a sum

3^{2} \times 6 x^{6 + 1}

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

3^{2} \times 6 x^{6} \times x

Reorder the terms

3^{2} x^{6} \times 6 x

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

3^{2} x^{6} \times 6 x

Reduce the index of the radical and exponent with 2

3 x^{3} 6 x

3 x^{3} 6 x = 0

Elimination the left coefficient

x^{3} 6 x = 0

Separate the equation into 2 possible cases

x^{3} = 0 6 x = 0

The only way a power can be 0 is when the base equals 0

x = 0 6 x = 0

Solve the equation

More Steps

Evaluate

6 x = 0

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

6 x = 0

Rewrite the expression

x = 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