Solve p^3508-69001 - Socratic AI (ScanMath)

Question

Simplify the expression

508 p^{3} - 69001

Evaluate

p^{3} \times 508 - 69001

Solution

508 p^{3} - 69001

Show Solution

p = \frac{3 69001 \times 50 8 ^{2}}{508}

Alternative Form

p \approx 5.140404

Evaluate

p^{3} \times 508 - 69001

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

p^{3} \times 508 - 69001 = 0

Use the commutative property to reorder the terms

508 p^{3} - 69001 = 0

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

508 p^{3} = 0 + 69001

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

508 p^{3} = 69001

Divide both sides

\frac{508 p ^{3}}{508} = \frac{69001}{508}

Divide the numbers

p^{3} = \frac{69001}{508}

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

3 p^{3} = 3 \frac{69001}{508}

Calculate

p = 3 \frac{69001}{508}

Solution

More Steps

Evaluate

3 \frac{69001}{508}

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

\frac{3 69001}{3 508}

Multiply by the Conjugate

\frac{3 69001 \times 3 50 8 ^{2}}{3 508 \times 3 50 8 ^{2}}

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

\frac{3 69001 \times 50 8 ^{2}}{3 508 \times 3 50 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

3508 \times 3 50 8^{2}

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

3 508 \times 50 8^{2}

Calculate the product

3 50 8^{3}

Reduce the index of the radical and exponent with 3

508

\frac{3 69001 \times 50 8 ^{2}}{508}

p = \frac{3 69001 \times 50 8 ^{2}}{508}

Alternative Form

p \approx 5.140404

Show Solution