Solve ( n 12n 1 ) n-1

Question

Simplify the expression

12 n^{3} - 1

Evaluate

(n \times 12 n \times 1) n - 1

Remove the parentheses

n \times 12 n \times 1 \times n - 1

Rewrite the expression in exponential form

n^{3} \times 12 \times 1 - 1

Solution

More Steps

Multiply the terms

n^{3} \times 12 \times 1

Rewrite the expression

n^{3} \times 12

Use the commutative property to reorder the terms

12 n^{3}

12 n^{3} - 1

Show Solution

n = \frac{3 18}{6}

Alternative Form

n \approx 0.43679

Evaluate

(n \times 12 n \times 1) n - 1

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

(n \times 12 n \times 1) n - 1 = 0

Multiply the terms

More Steps

Multiply the terms

n \times 12 n \times 1

Rewrite the expression

n \times 12 n

Multiply the terms

n^{2} \times 12

Use the commutative property to reorder the terms

12 n^{2}

12 n^{2} \times n - 1 = 0

Multiply the terms

More Steps

Evaluate

n^{2} \times n

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

n^{2 + 1}

Add the numbers

n^{3}

12 n^{3} - 1 = 0

Move the constant to the right-hand side and change its sign

12 n^{3} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

12 n^{3} = 1

Divide both sides

\frac{12 n ^{3}}{12} = \frac{1}{12}

Divide the numbers

n^{3} = \frac{1}{12}

Take the 3 -th root on both sides of the equation

3 n^{3} = 3 \frac{1}{12}

Calculate

n = 3 \frac{1}{12}

Solution

More Steps

Evaluate

3 \frac{1}{12}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 12}

Simplify the radical expression

\frac{1}{3 12}

Multiply by the Conjugate

\frac{3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 3 1 2^{2}

The product of roots with the same index is equal to the root of the product

3 12 \times 1 2^{2}

Calculate the product

3 1 2^{3}

Reduce the index of the radical and exponent with 3

12

\frac{2 3 18}{12}

Cancel out the common factor 2

\frac{3 18}{6}

n = \frac{3 18}{6}

Alternative Form

n \approx 0.43679

Show Solution