Solve m^3100-2002025

Question

Simplify the expression

100 m^{3} - 2002025

Evaluate

m^{3} \times 100 - 2002025

Solution

100 m^{3} - 2002025

Show Solution

25 (4 m^{3} - 80081)

Evaluate

m^{3} \times 100 - 2002025

Use the commutative property to reorder the terms

100 m^{3} - 2002025

Solution

25 (4 m^{3} - 80081)

Show Solution

m = \frac{3 160162}{2}

Alternative Form

m \approx 27.153334

Evaluate

m^{3} \times 100 - 2002025

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

m^{3} \times 100 - 2002025 = 0

Use the commutative property to reorder the terms

100 m^{3} - 2002025 = 0

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

100 m^{3} = 0 + 2002025

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

100 m^{3} = 2002025

Divide both sides

\frac{100 m ^{3}}{100} = \frac{2002025}{100}

Divide the numbers

m^{3} = \frac{2002025}{100}

Cancel out the common factor 25

m^{3} = \frac{80081}{4}

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

3 m^{3} = 3 \frac{80081}{4}

Calculate

m = 3 \frac{80081}{4}

Solution

More Steps

Evaluate

3 \frac{80081}{4}

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

\frac{3 80081}{3 4}

Multiply by the Conjugate

\frac{3 80081 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{3 80081 \times 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

380081 \times 232

Multiply the terms

3160162 \times 2

Use the commutative property to reorder the terms

23160162

\frac{2 3 160162}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 160162}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 160162}{2}

m = \frac{3 160162}{2}

Alternative Form

m \approx 27.153334

Show Solution