Solve n^2 59n-900

Question

Simplify the expression

59 n^{3} - 900

Evaluate

n^{2} \times 59 n - 900

Solution

More Steps

Evaluate

n^{2} \times 59 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 59

Add the numbers

n^{3} \times 59

Use the commutative property to reorder the terms

59 n^{3}

59 n^{3} - 900

Show Solution

n = \frac{3 3132900}{59}

Alternative Form

n \approx 2.480067

Evaluate

n^{2} \times 59 n - 900

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

n^{2} \times 59 n - 900 = 0

Multiply

More Steps

Multiply the terms

n^{2} \times 59 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 59

Add the numbers

n^{3} \times 59

Use the commutative property to reorder the terms

59 n^{3}

59 n^{3} - 900 = 0

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

59 n^{3} = 0 + 900

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

59 n^{3} = 900

Divide both sides

\frac{59 n ^{3}}{59} = \frac{900}{59}

Divide the numbers

n^{3} = \frac{900}{59}

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

3 n^{3} = 3 \frac{900}{59}

Calculate

n = 3 \frac{900}{59}

Solution

More Steps

Evaluate

3 \frac{900}{59}

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

\frac{3 900}{3 59}

Multiply by the Conjugate

\frac{3 900 \times 3 5 9 ^{2}}{3 59 \times 3 5 9 ^{2}}

Simplify

\frac{3 900 \times 3 3481}{3 59 \times 3 5 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

3900 \times 33481

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

3 900 \times 3481

Calculate the product

33132900

\frac{3 3132900}{3 59 \times 3 5 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

359 \times 3 5 9^{2}

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

3 59 \times 5 9^{2}

Calculate the product

3 5 9^{3}

Reduce the index of the radical and exponent with 3

59

\frac{3 3132900}{59}

n = \frac{3 3132900}{59}

Alternative Form

n \approx 2.480067

Show Solution