Solve h^3256-4 - Socratic AI (ScanMath)

Question

Simplify the expression

256 h^{3} - 4

Evaluate

h^{3} \times 256 - 4

Solution

256 h^{3} - 4

Show Solution

4 (4 h - 1) (16 h^{2} + 4 h + 1)

Evaluate

h^{3} \times 256 - 4

Use the commutative property to reorder the terms

256 h^{3} - 4

Factor out 4 from the expression

4 (64 h^{3} - 1)

Solution

More Steps

Evaluate

64 h^{3} - 1

Rewrite the expression in exponential form

(4 h)^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(4 h - 1) ((4 h)^{2} + 4 h \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(4 h)^{2}

To raise a product to a power,raise each factor to that power

4^{2} h^{2}

Evaluate the power

16 h^{2}

(4 h - 1) (16 h^{2} + 4 h \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(4 h - 1) (16 h^{2} + 4 h + 1^{2})

1 raised to any power equals to 1

(4 h - 1) (16 h^{2} + 4 h + 1)

4 (4 h - 1) (16 h^{2} + 4 h + 1)

Show Solution

h = \frac{1}{4}

Alternative Form

h = 0.25

Evaluate

h^{3} \times 256 - 4

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

h^{3} \times 256 - 4 = 0

Use the commutative property to reorder the terms

256 h^{3} - 4 = 0

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

256 h^{3} = 0 + 4

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

256 h^{3} = 4

Divide both sides

\frac{256 h ^{3}}{256} = \frac{4}{256}

Divide the numbers

h^{3} = \frac{4}{256}

Cancel out the common factor 4

h^{3} = \frac{1}{64}

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

3 h^{3} = 3 \frac{1}{64}

Calculate

h = 3 \frac{1}{64}

Solution

More Steps

Evaluate

3 \frac{1}{64}

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

\frac{3 1}{3 64}

Simplify the radical expression

\frac{1}{3 64}

Simplify the radical expression

More Steps

Evaluate

364

Write the number in exponential form with the base of 4

3 4^{3}

Reduce the index of the radical and exponent with 3

4

\frac{1}{4}

h = \frac{1}{4}

Alternative Form

h = 0.25

Show Solution