Solve sqrt(360035x^35)

Question

Simplify the expression

5 x 72007 x

Evaluate

360035 x^{3} \times 5

Multiply the terms

1800175 x^{3}

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

25 \times 72007 x^{3}

Write the number in exponential form with the base of 5

5^{2} \times 72007 x^{3}

Rewrite the exponent as a sum

5^{2} \times 72007 x^{2 + 1}

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

5^{2} \times 72007 x^{2} \times x

Reorder the terms

5^{2} x^{2} \times 72007 x

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

5^{2} x^{2} \times 72007 x

Solution

5 x 72007 x

Show Solution

x = 0

Evaluate

360035 x^{3} \times 5

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

360035 x^{3} \times 5 = 0

Find the domain

More Steps

Evaluate

360035 x^{3} \times 5 \geq 0

Multiply the terms

1800175 x^{3} \geq 0

Rewrite the expression

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

360035 x^{3} \times 5 = 0, x \geq 0

Calculate

360035 x^{3} \times 5 = 0

Multiply the terms

1800175 x^{3} = 0

Simplify the root

More Steps

Evaluate

1800175 x^{3}

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

25 \times 72007 x^{3}

Write the number in exponential form with the base of 5

5^{2} \times 72007 x^{3}

Rewrite the exponent as a sum

5^{2} \times 72007 x^{2 + 1}

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

5^{2} \times 72007 x^{2} \times x

Reorder the terms

5^{2} x^{2} \times 72007 x

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

5^{2} x^{2} \times 72007 x

Reduce the index of the radical and exponent with 2

5 x 72007 x

5 x 72007 x = 0

Elimination the left coefficient

x 72007 x = 0

Separate the equation into 2 possible cases

x = 0 72007 x = 0

Solve the equation

More Steps

Evaluate

72007 x = 0

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

72007 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