Solve 1 4/5= x^3/8

Question

Solve the equation

x = \frac{2 3 225}{5}

Alternative Form

x \approx 2.432881

Evaluate

1 \frac{4}{5} = \frac{x ^{3}}{8}

Covert the mixed number to an improper fraction

More Steps

Evaluate

1 \frac{4}{5}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 + 4}{5}

Add the terms

\frac{9}{5}

\frac{9}{5} = \frac{x ^{3}}{8}

Swap the sides of the equation

\frac{x ^{3}}{8} = \frac{9}{5}

Multiply both sides of the equation by 8

\frac{x ^{3}}{8} \times 8 = \frac{9}{5} \times 8

Multiply the terms

x^{3} = \frac{9 \times 8}{5}

Divide the terms

x^{3} = \frac{72}{5}

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

3 x^{3} = 3 \frac{72}{5}

Calculate

x = 3 \frac{72}{5}

Solution

More Steps

Evaluate

3 \frac{72}{5}

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

\frac{3 72}{3 5}

Simplify the radical expression

More Steps

Evaluate

372

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

3 8 \times 9

Write the number in exponential form with the base of 2

3 2^{3} \times 9

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

3 2^{3} \times 39

Reduce the index of the radical and exponent with 3

239

\frac{2 3 9}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{2 3 9 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 325

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

3 9 \times 25

Calculate the product

3225

\frac{2 3 225}{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 3 225}{5}

x = \frac{2 3 225}{5}

Alternative Form

x \approx 2.432881

Show Solution