Solve m^39006/25-180

Question

Simplify the expression

\frac{9006}{25} m^{3} - 180

Evaluate

m^{3} \times \frac{9006}{25} - 180

Solution

\frac{9006}{25} m^{3} - 180

Show Solution

\frac{6}{25} (1501 m^{3} - 750)

Evaluate

m^{3} \times \frac{9006}{25} - 180

Use the commutative property to reorder the terms

\frac{9006}{25} m^{3} - 180

Solution

\frac{6}{25} (1501 m^{3} - 750)

Show Solution

m = \frac{5 3 6 \times 150 1 ^{2}}{1501}

Alternative Form

m \approx 0.793524

Evaluate

m^{3} \times \frac{9006}{25} - 180

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

m^{3} \times \frac{9006}{25} - 180 = 0

Use the commutative property to reorder the terms

\frac{9006}{25} m^{3} - 180 = 0

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

\frac{9006}{25} m^{3} = 0 + 180

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

\frac{9006}{25} m^{3} = 180

Multiply by the reciprocal

\frac{9006}{25} m^{3} \times \frac{25}{9006} = 180 \times \frac{25}{9006}

Multiply

m^{3} = 180 \times \frac{25}{9006}

Multiply

More Steps

Evaluate

180 \times \frac{25}{9006}

Reduce the numbers

30 \times \frac{25}{1501}

Multiply the numbers

\frac{30 \times 25}{1501}

Multiply the numbers

\frac{750}{1501}

m^{3} = \frac{750}{1501}

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

3 m^{3} = 3 \frac{750}{1501}

Calculate

m = 3 \frac{750}{1501}

Solution

More Steps

Evaluate

3 \frac{750}{1501}

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

\frac{3 750}{3 1501}

Simplify the radical expression

More Steps

Evaluate

3750

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

3 125 \times 6

Write the number in exponential form with the base of 5

3 5^{3} \times 6

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

3 5^{3} \times 36

Reduce the index of the radical and exponent with 3

536

\frac{5 3 6}{3 1501}

Multiply by the Conjugate

\frac{5 3 6 \times 3 150 1 ^{2}}{3 1501 \times 3 150 1 ^{2}}

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

\frac{5 3 6 \times 150 1 ^{2}}{3 1501 \times 3 150 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

31501 \times 3 150 1^{2}

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

3 1501 \times 150 1^{2}

Calculate the product

3 150 1^{3}

Reduce the index of the radical and exponent with 3

1501

\frac{5 3 6 \times 150 1 ^{2}}{1501}

m = \frac{5 3 6 \times 150 1 ^{2}}{1501}

Alternative Form

m \approx 0.793524

Show Solution