Solve M^39019/2-224

Question

Simplify the expression

\frac{9019}{2} M^{3} - 224

Evaluate

M^{3} \times \frac{9019}{2} - 224

Solution

\frac{9019}{2} M^{3} - 224

Show Solution

\frac{1}{2} (9019 M^{3} - 448)

Evaluate

M^{3} \times \frac{9019}{2} - 224

Use the commutative property to reorder the terms

\frac{9019}{2} M^{3} - 224

Solution

\frac{1}{2} (9019 M^{3} - 448)

Show Solution

M = \frac{4 3 7 \times 901 9 ^{2}}{9019}

Alternative Form

M \approx 0.367598

Evaluate

M^{3} \times \frac{9019}{2} - 224

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

M^{3} \times \frac{9019}{2} - 224 = 0

Use the commutative property to reorder the terms

\frac{9019}{2} M^{3} - 224 = 0

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

\frac{9019}{2} M^{3} = 0 + 224

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

\frac{9019}{2} M^{3} = 224

Multiply by the reciprocal

\frac{9019}{2} M^{3} \times \frac{2}{9019} = 224 \times \frac{2}{9019}

Multiply

M^{3} = 224 \times \frac{2}{9019}

Multiply

More Steps

Evaluate

224 \times \frac{2}{9019}

Multiply the numbers

\frac{224 \times 2}{9019}

Multiply the numbers

\frac{448}{9019}

M^{3} = \frac{448}{9019}

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

3 M^{3} = 3 \frac{448}{9019}

Calculate

M = 3 \frac{448}{9019}

Solution

More Steps

Evaluate

3 \frac{448}{9019}

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

\frac{3 448}{3 9019}

Simplify the radical expression

More Steps

Evaluate

3448

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

3 64 \times 7

Write the number in exponential form with the base of 4

3 4^{3} \times 7

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

3 4^{3} \times 37

Reduce the index of the radical and exponent with 3

437

\frac{4 3 7}{3 9019}

Multiply by the Conjugate

\frac{4 3 7 \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{4 3 7 \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{4 3 7 \times 901 9 ^{2}}{9019}

M = \frac{4 3 7 \times 901 9 ^{2}}{9019}

Alternative Form

M \approx 0.367598

Show Solution