Solve 2n^2 n - 517

Question

Simplify the expression

2 n^{3} - 517

Evaluate

2 n^{2} \times n - 517

Solution

More Steps

Evaluate

2 n^{2} \times n

Multiply the terms with the same base by adding their exponents

2 n^{2 + 1}

Add the numbers

2 n^{3}

2 n^{3} - 517

Show Solution

n = \frac{3 2068}{2}

Alternative Form

n \approx 6.370207

Evaluate

2 n^{2} \times n - 517

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

2 n^{2} \times n - 517 = 0

Multiply

More Steps

Multiply the terms

2 n^{2} \times n

Multiply the terms with the same base by adding their exponents

2 n^{2 + 1}

Add the numbers

2 n^{3}

2 n^{3} - 517 = 0

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

2 n^{3} = 0 + 517

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

2 n^{3} = 517

Divide both sides

\frac{2 n ^{3}}{2} = \frac{517}{2}

Divide the numbers

n^{3} = \frac{517}{2}

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

3 n^{3} = 3 \frac{517}{2}

Calculate

n = 3 \frac{517}{2}

Solution

More Steps

Evaluate

3 \frac{517}{2}

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

\frac{3 517}{3 2}

Multiply by the Conjugate

\frac{3 517 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 517 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3517 \times 34

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

3 517 \times 4

Calculate the product

32068

\frac{3 2068}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 2068}{2}

n = \frac{3 2068}{2}

Alternative Form

n \approx 6.370207

Show Solution