Solve M^39019/3-216

Question

Simplify the expression

\frac{9019}{3} M^{3} - 216

Evaluate

M^{3} \times \frac{9019}{3} - 216

Solution

\frac{9019}{3} M^{3} - 216

Show Solution

\frac{1}{3} (9019 M^{3} - 648)

Evaluate

M^{3} \times \frac{9019}{3} - 216

Use the commutative property to reorder the terms

\frac{9019}{3} M^{3} - 216

Solution

\frac{1}{3} (9019 M^{3} - 648)

Show Solution

M = \frac{6 3 3 \times 901 9 ^{2}}{9019}

Alternative Form

M \approx 0.415724

Evaluate

M^{3} \times \frac{9019}{3} - 216

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

M^{3} \times \frac{9019}{3} - 216 = 0

Use the commutative property to reorder the terms

\frac{9019}{3} M^{3} - 216 = 0

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

\frac{9019}{3} M^{3} = 0 + 216

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

\frac{9019}{3} M^{3} = 216

Multiply by the reciprocal

\frac{9019}{3} M^{3} \times \frac{3}{9019} = 216 \times \frac{3}{9019}

Multiply

M^{3} = 216 \times \frac{3}{9019}

Multiply

More Steps

Evaluate

216 \times \frac{3}{9019}

Multiply the numbers

\frac{216 \times 3}{9019}

Multiply the numbers

\frac{648}{9019}

M^{3} = \frac{648}{9019}

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

3 M^{3} = 3 \frac{648}{9019}

Calculate

M = 3 \frac{648}{9019}

Solution

More Steps

Evaluate

3 \frac{648}{9019}

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

\frac{3 648}{3 9019}

Simplify the radical expression

More Steps

Evaluate

3648

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

3 216 \times 3

Write the number in exponential form with the base of 6

3 6^{3} \times 3

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

3 6^{3} \times 33

Reduce the index of the radical and exponent with 3

633

\frac{6 3 3}{3 9019}

Multiply by the Conjugate

\frac{6 3 3 \times 3 901 9 ^{2}}{3 9019 \times 3 901 9 ^{2}}

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

\frac{6 3 3 \times 901 9 ^{2}}{3 9019 \times 3 901 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39019 \times 3 901 9^{2}

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

3 9019 \times 901 9^{2}

Calculate the product

3 901 9^{3}

Reduce the index of the radical and exponent with 3

9019

\frac{6 3 3 \times 901 9 ^{2}}{9019}

M = \frac{6 3 3 \times 901 9 ^{2}}{9019}

Alternative Form

M \approx 0.415724

Show Solution