Solve M^39018/4-33

Question

Simplify the expression

\frac{4509}{2} M^{3} - 33

Evaluate

M^{3} \times \frac{9018}{4} - 33

Cancel out the common factor 2

M^{3} \times \frac{4509}{2} - 33

Solution

\frac{4509}{2} M^{3} - 33

Show Solution

\frac{3}{2} (1503 M^{3} - 22)

Evaluate

M^{3} \times \frac{9018}{4} - 33

Cancel out the common factor 2

M^{3} \times \frac{4509}{2} - 33

Use the commutative property to reorder the terms

\frac{4509}{2} M^{3} - 33

Solution

\frac{3}{2} (1503 M^{3} - 22)

Show Solution

M = \frac{3 22 \times 150 3 ^{2}}{1503}

Alternative Form

M \approx 0.244618

Evaluate

M^{3} \times \frac{9018}{4} - 33

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

M^{3} \times \frac{9018}{4} - 33 = 0

Cancel out the common factor 2

M^{3} \times \frac{4509}{2} - 33 = 0

Use the commutative property to reorder the terms

\frac{4509}{2} M^{3} - 33 = 0

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

\frac{4509}{2} M^{3} = 0 + 33

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

\frac{4509}{2} M^{3} = 33

Multiply by the reciprocal

\frac{4509}{2} M^{3} \times \frac{2}{4509} = 33 \times \frac{2}{4509}

Multiply

M^{3} = 33 \times \frac{2}{4509}

Multiply

More Steps

Evaluate

33 \times \frac{2}{4509}

Reduce the numbers

11 \times \frac{2}{1503}

Multiply the numbers

\frac{11 \times 2}{1503}

Multiply the numbers

\frac{22}{1503}

M^{3} = \frac{22}{1503}

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

3 M^{3} = 3 \frac{22}{1503}

Calculate

M = 3 \frac{22}{1503}

Solution

More Steps

Evaluate

3 \frac{22}{1503}

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

\frac{3 22}{3 1503}

Multiply by the Conjugate

\frac{3 22 \times 3 150 3 ^{2}}{3 1503 \times 3 150 3 ^{2}}

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

\frac{3 22 \times 150 3 ^{2}}{3 1503 \times 3 150 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

31503 \times 3 150 3^{2}

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

3 1503 \times 150 3^{2}

Calculate the product

3 150 3^{3}

Reduce the index of the radical and exponent with 3

1503

\frac{3 22 \times 150 3 ^{2}}{1503}

M = \frac{3 22 \times 150 3 ^{2}}{1503}

Alternative Form

M \approx 0.244618

Show Solution