Solve m^39006/2-1311

Question

Simplify the expression

4503 m^{3} - 1311

Evaluate

m^{3} \times \frac{9006}{2} - 1311

Divide the terms

More Steps

Evaluate

\frac{9006}{2}

Reduce the numbers

\frac{4503}{1}

Calculate

4503

m^{3} \times 4503 - 1311

Solution

4503 m^{3} - 1311

Show Solution

Factor the expression

57 (79 m^{3} - 23)

Evaluate

m^{3} \times \frac{9006}{2} - 1311

Divide the terms

More Steps

Evaluate

\frac{9006}{2}

Reduce the numbers

\frac{4503}{1}

Calculate

4503

m^{3} \times 4503 - 1311

Use the commutative property to reorder the terms

4503 m^{3} - 1311

Solution

57 (79 m^{3} - 23)

Show Solution

Find the roots

m = \frac{3 143543}{79}

Alternative Form

m \approx 0.662776

Evaluate

m^{3} \times \frac{9006}{2} - 1311

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

m^{3} \times \frac{9006}{2} - 1311 = 0

Divide the terms

More Steps

Evaluate

\frac{9006}{2}

Reduce the numbers

\frac{4503}{1}

Calculate

4503

m^{3} \times 4503 - 1311 = 0

Use the commutative property to reorder the terms

4503 m^{3} - 1311 = 0

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

4503 m^{3} = 0 + 1311

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

4503 m^{3} = 1311

Divide both sides

\frac{4503 m ^{3}}{4503} = \frac{1311}{4503}

Divide the numbers

m^{3} = \frac{1311}{4503}

Cancel out the common factor 57

m^{3} = \frac{23}{79}

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

3 m^{3} = 3 \frac{23}{79}

Calculate

m = 3 \frac{23}{79}

Solution

More Steps

Evaluate

3 \frac{23}{79}

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

\frac{3 23}{3 79}

Multiply by the Conjugate

\frac{3 23 \times 3 7 9 ^{2}}{3 79 \times 3 7 9 ^{2}}

Simplify

\frac{3 23 \times 3 6241}{3 79 \times 3 7 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

323 \times 36241

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

3 23 \times 6241

Calculate the product

3143543

\frac{3 143543}{3 79 \times 3 7 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

379 \times 3 7 9^{2}

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

3 79 \times 7 9^{2}

Calculate the product

3 7 9^{3}

Reduce the index of the radical and exponent with 3

79

\frac{3 143543}{79}

m = \frac{3 143543}{79}

Alternative Form

m \approx 0.662776

Show Solution