Solve p^2 11p - 1

Question

Simplify the expression

11 p^{3} - 1

Evaluate

p^{2} \times 11 p - 1

Solution

More Steps

Evaluate

p^{2} \times 11 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 11

Add the numbers

p^{3} \times 11

Use the commutative property to reorder the terms

11 p^{3}

11 p^{3} - 1

Show Solution

p = \frac{3 121}{11}

Alternative Form

p \approx 0.449644

Evaluate

p^{2} \times 11 p - 1

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

p^{2} \times 11 p - 1 = 0

Multiply

More Steps

Multiply the terms

p^{2} \times 11 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 11

Add the numbers

p^{3} \times 11

Use the commutative property to reorder the terms

11 p^{3}

11 p^{3} - 1 = 0

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

11 p^{3} = 0 + 1

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

11 p^{3} = 1

Divide both sides

\frac{11 p ^{3}}{11} = \frac{1}{11}

Divide the numbers

p^{3} = \frac{1}{11}

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

3 p^{3} = 3 \frac{1}{11}

Calculate

p = 3 \frac{1}{11}

Solution

More Steps

Evaluate

3 \frac{1}{11}

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

\frac{3 1}{3 11}

Simplify the radical expression

\frac{1}{3 11}

Multiply by the Conjugate

\frac{3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3 1 1^{2}

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

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{3 121}{11}

p = \frac{3 121}{11}

Alternative Form

p \approx 0.449644

Show Solution