Solve s^3-6s^2 5s^48

Question

Simplify the expression

s^{3} - 240 s^{6}

Evaluate

s^{3} - 6 s^{2} \times 5 s^{4} \times 8

Solution

More Steps

Evaluate

6 s^{2} \times 5 s^{4} \times 8

Multiply the terms

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Evaluate

6 \times 5 \times 8

Multiply the terms

30 \times 8

Multiply the numbers

240

240 s^{2} \times s^{4}

Multiply the terms with the same base by adding their exponents

240 s^{2 + 4}

Add the numbers

240 s^{6}

s^{3} - 240 s^{6}

Show Solution

Factor the expression

s^{3} (1 - 240 s^{3})

Evaluate

s^{3} - 6 s^{2} \times 5 s^{4} \times 8

Multiply

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Evaluate

6 s^{2} \times 5 s^{4} \times 8

Multiply the terms

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Evaluate

6 \times 5 \times 8

Multiply the terms

30 \times 8

Multiply the numbers

240

240 s^{2} \times s^{4}

Multiply the terms with the same base by adding their exponents

240 s^{2 + 4}

Add the numbers

240 s^{6}

s^{3} - 240 s^{6}

Rewrite the expression

s^{3} - s^{3} \times 240 s^{3}

Solution

s^{3} (1 - 240 s^{3})

Show Solution

Find the roots

s_{1} = 0, s_{2} = \frac{3 900}{60}

Alternative Form

s_{1} = 0, s_{2} \approx 0.160915

Evaluate

s^{3} - 6 s^{2} \times 5 s^{4} \times 8

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

s^{3} - 6 s^{2} \times 5 s^{4} \times 8 = 0

Multiply

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Multiply the terms

6 s^{2} \times 5 s^{4} \times 8

Multiply the terms

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Evaluate

6 \times 5 \times 8

Multiply the terms

30 \times 8

Multiply the numbers

240

240 s^{2} \times s^{4}

Multiply the terms with the same base by adding their exponents

240 s^{2 + 4}

Add the numbers

240 s^{6}

s^{3} - 240 s^{6} = 0

Factor the expression

s^{3} (1 - 240 s^{3}) = 0

Separate the equation into 2 possible cases

s^{3} = 0 1 - 240 s^{3} = 0

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

s = 0 1 - 240 s^{3} = 0

Solve the equation

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Evaluate

1 - 240 s^{3} = 0

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

- 240 s^{3} = 0 - 1

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

- 240 s^{3} = - 1

Change the signs on both sides of the equation

240 s^{3} = 1

Divide both sides

\frac{240 s ^{3}}{240} = \frac{1}{240}

Divide the numbers

s^{3} = \frac{1}{240}

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

3 s^{3} = 3 \frac{1}{240}

Calculate

s = 3 \frac{1}{240}

Simplify the root

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Evaluate

3 \frac{1}{240}

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

\frac{3 1}{3 240}

Simplify the radical expression

\frac{1}{3 240}

Simplify the radical expression

\frac{1}{2 3 30}

Multiply by the Conjugate

\frac{3 3 0 ^{2}}{2 3 30 \times 3 3 0 ^{2}}

Simplify

\frac{3 900}{2 3 30 \times 3 3 0 ^{2}}

Multiply the numbers

\frac{3 900}{60}

s = \frac{3 900}{60}

s = 0 s = \frac{3 900}{60}

Solution

s_{1} = 0, s_{2} = \frac{3 900}{60}

Alternative Form

s_{1} = 0, s_{2} \approx 0.160915

Show Solution