Solve 31p^3+15 - ScanMath

Question

Find the roots

p = - \frac{3 14415}{31}

Alternative Form

p \approx - 0.785073

Evaluate

31 p^{3} + 15

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

31 p^{3} + 15 = 0

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

31 p^{3} = 0 - 15

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

31 p^{3} = - 15

Divide both sides

\frac{31 p ^{3}}{31} = \frac{- 15}{31}

Divide the numbers

p^{3} = \frac{- 15}{31}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

p^{3} = - \frac{15}{31}

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

3 p^{3} = 3 - \frac{15}{31}

Calculate

p = 3 - \frac{15}{31}

Solution

More Steps

Evaluate

3 - \frac{15}{31}

An odd root of a negative radicand is always a negative

- 3 \frac{15}{31}

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

- \frac{3 15}{3 31}

Multiply by the Conjugate

\frac{- 3 15 \times 3 3 1 ^{2}}{3 31 \times 3 3 1 ^{2}}

Simplify

\frac{- 3 15 \times 3 961}{3 31 \times 3 3 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 315 \times 3961

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

- 3 15 \times 961

Calculate the product

- 314415

\frac{- 3 14415}{3 31 \times 3 3 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

331 \times 3 3 1^{2}

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

3 31 \times 3 1^{2}

Calculate the product

3 3 1^{3}

Reduce the index of the radical and exponent with 3

31

\frac{- 3 14415}{31}

Calculate

- \frac{3 14415}{31}

p = - \frac{3 14415}{31}

Alternative Form

p \approx - 0.785073

Show Solution