Solve (5x^3)/2 =24

Question

Solve the equation

x = \frac{2 3 150}{5}

Alternative Form

x \approx 2.125317

Evaluate

\frac{5 x ^{3}}{2} = 24

Cross multiply

5 x^{3} = 2 \times 24

Simplify the equation

5 x^{3} = 48

Divide both sides

\frac{5 x ^{3}}{5} = \frac{48}{5}

Divide the numbers

x^{3} = \frac{48}{5}

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

3 x^{3} = 3 \frac{48}{5}

Calculate

x = 3 \frac{48}{5}

Solution

More Steps

Evaluate

3 \frac{48}{5}

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

\frac{3 48}{3 5}

Simplify the radical expression

More Steps

Evaluate

348

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

\frac{2 3 6}{3 5}

Multiply by the Conjugate

\frac{2 3 6 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{2 3 6 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 325

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

3 6 \times 25

Calculate the product

3150

\frac{2 3 150}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{2 3 150}{5}

x = \frac{2 3 150}{5}

Alternative Form

x \approx 2.125317

Show Solution