Solve n^310-100-1018

Question

Simplify the expression

10 n^{3} - 1118

Evaluate

n^{3} \times 10 - 100 - 1018

Use the commutative property to reorder the terms

10 n^{3} - 100 - 1018

Solution

10 n^{3} - 1118

Show Solution

2 (5 n^{3} - 559)

Evaluate

n^{3} \times 10 - 100 - 1018

Use the commutative property to reorder the terms

10 n^{3} - 100 - 1018

Subtract the numbers

10 n^{3} - 1118

Solution

2 (5 n^{3} - 559)

Show Solution

n = \frac{3 13975}{5}

Alternative Form

n \approx 4.817414

Evaluate

n^{3} \times 10 - 100 - 1018

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

n^{3} \times 10 - 100 - 1018 = 0

Use the commutative property to reorder the terms

10 n^{3} - 100 - 1018 = 0

Subtract the numbers

10 n^{3} - 1118 = 0

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

10 n^{3} = 0 + 1118

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

10 n^{3} = 1118

Divide both sides

\frac{10 n ^{3}}{10} = \frac{1118}{10}

Divide the numbers

n^{3} = \frac{1118}{10}

Cancel out the common factor 2

n^{3} = \frac{559}{5}

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

3 n^{3} = 3 \frac{559}{5}

Calculate

n = 3 \frac{559}{5}

Solution

More Steps

Evaluate

3 \frac{559}{5}

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

\frac{3 559}{3 5}

Multiply by the Conjugate

\frac{3 559 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 559 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

3559 \times 325

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

3 559 \times 25

Calculate the product

313975

\frac{3 13975}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 13975}{5}

n = \frac{3 13975}{5}

Alternative Form

n \approx 4.817414

Show Solution