Solve \sqrt{48n^5}

Question

Simplify the expression

4 n^{2} 3 n

Evaluate

48 n^{5}

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

16 \times 3 n^{5}

Write the number in exponential form with the base of 4

4^{2} \times 3 n^{5}

Rewrite the exponent as a sum

4^{2} \times 3 n^{4 + 1}

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

4^{2} \times 3 n^{4} \times n

Reorder the terms

4^{2} n^{4} \times 3 n

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

4^{2} n^{4} \times 3 n

Solution

4 n^{2} 3 n

Show Solution

n = 0

Evaluate

48 n^{5}

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

48 n^{5} = 0

Find the domain

More Steps

Evaluate

48 n^{5} \geq 0

Rewrite the expression

n^{5} \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

n \geq 0

48 n^{5} = 0, n \geq 0

Calculate

48 n^{5} = 0

Simplify the root

More Steps

Evaluate

48 n^{5}

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

16 \times 3 n^{5}

Write the number in exponential form with the base of 4

4^{2} \times 3 n^{5}

Rewrite the exponent as a sum

4^{2} \times 3 n^{4 + 1}

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

4^{2} \times 3 n^{4} \times n

Reorder the terms

4^{2} n^{4} \times 3 n

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

4^{2} n^{4} \times 3 n

Reduce the index of the radical and exponent with 2

4 n^{2} 3 n

4 n^{2} 3 n = 0

Elimination the left coefficient

n^{2} 3 n = 0

Separate the equation into 2 possible cases

n^{2} = 0 3 n = 0

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

n = 0 3 n = 0

Solve the equation

More Steps

Evaluate

3 n = 0

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

3 n = 0

Rewrite the expression

n = 0

n = 0 n = 0

Find the union

n = 0

Check if the solution is in the defined range

n = 0, n \geq 0

Solution

n = 0

Show Solution