Solve 5n^227n-770

Question

Simplify the expression

135 n^{3} - 770

Evaluate

5 n^{2} \times 27 n - 770

Solution

More Steps

Evaluate

5 n^{2} \times 27 n

Multiply the terms

135 n^{2} \times n

Multiply the terms with the same base by adding their exponents

135 n^{2 + 1}

Add the numbers

135 n^{3}

135 n^{3} - 770

Show Solution

5 (27 n^{3} - 154)

Evaluate

5 n^{2} \times 27 n - 770

Multiply

More Steps

Evaluate

5 n^{2} \times 27 n

Multiply the terms

135 n^{2} \times n

Multiply the terms with the same base by adding their exponents

135 n^{2 + 1}

Add the numbers

135 n^{3}

135 n^{3} - 770

Solution

5 (27 n^{3} - 154)

Show Solution

n = \frac{3 154}{3}

Alternative Form

n \approx 1.786703

Evaluate

5 n^{2} \times 27 n - 770

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

5 n^{2} \times 27 n - 770 = 0

Multiply

More Steps

Multiply the terms

5 n^{2} \times 27 n

Multiply the terms

135 n^{2} \times n

Multiply the terms with the same base by adding their exponents

135 n^{2 + 1}

Add the numbers

135 n^{3}

135 n^{3} - 770 = 0

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

135 n^{3} = 0 + 770

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

135 n^{3} = 770

Divide both sides

\frac{135 n ^{3}}{135} = \frac{770}{135}

Divide the numbers

n^{3} = \frac{770}{135}

Cancel out the common factor 5

n^{3} = \frac{154}{27}

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

3 n^{3} = 3 \frac{154}{27}

Calculate

n = 3 \frac{154}{27}

Solution

More Steps

Evaluate

3 \frac{154}{27}

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

\frac{3 154}{3 27}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 154}{3}

n = \frac{3 154}{3}

Alternative Form

n \approx 1.786703

Show Solution