Solve b^36-2001/157

Question

Simplify the expression

6 b^{3} - \frac{2001}{157}

Evaluate

b^{3} \times 6 - \frac{2001}{157}

Solution

6 b^{3} - \frac{2001}{157}

Show Solution

\frac{3}{157} (314 b^{3} - 667)

Evaluate

b^{3} \times 6 - \frac{2001}{157}

Use the commutative property to reorder the terms

6 b^{3} - \frac{2001}{157}

Solution

\frac{3}{157} (314 b^{3} - 667)

Show Solution

b = \frac{3 667 \times 31 4 ^{2}}{314}

Alternative Form

b \approx 1.28548

Evaluate

b^{3} \times 6 - \frac{2001}{157}

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

b^{3} \times 6 - \frac{2001}{157} = 0

Use the commutative property to reorder the terms

6 b^{3} - \frac{2001}{157} = 0

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

6 b^{3} = 0 + \frac{2001}{157}

Add the terms

6 b^{3} = \frac{2001}{157}

Multiply by the reciprocal

6 b^{3} \times \frac{1}{6} = \frac{2001}{157} \times \frac{1}{6}

Multiply

b^{3} = \frac{2001}{157} \times \frac{1}{6}

Multiply

More Steps

Evaluate

\frac{2001}{157} \times \frac{1}{6}

Reduce the numbers

\frac{667}{157} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{667}{157 \times 2}

Multiply the numbers

\frac{667}{314}

b^{3} = \frac{667}{314}

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

3 b^{3} = 3 \frac{667}{314}

Calculate

b = 3 \frac{667}{314}

Solution

More Steps

Evaluate

3 \frac{667}{314}

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

\frac{3 667}{3 314}

Multiply by the Conjugate

\frac{3 667 \times 3 31 4 ^{2}}{3 314 \times 3 31 4 ^{2}}

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

\frac{3 667 \times 31 4 ^{2}}{3 314 \times 3 31 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

3314 \times 3 31 4^{2}

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

3 314 \times 31 4^{2}

Calculate the product

3 31 4^{3}

Reduce the index of the radical and exponent with 3

314

\frac{3 667 \times 31 4 ^{2}}{314}

b = \frac{3 667 \times 31 4 ^{2}}{314}

Alternative Form

b \approx 1.28548

Show Solution