Solve m^3200-10100

Question

Simplify the expression

200 m^{3} - 10100

Evaluate

m^{3} \times 200 - 10100

Solution

200 m^{3} - 10100

Show Solution

100 (2 m^{3} - 101)

Evaluate

m^{3} \times 200 - 10100

Use the commutative property to reorder the terms

200 m^{3} - 10100

Solution

100 (2 m^{3} - 101)

Show Solution

m = \frac{3 404}{2}

Alternative Form

m \approx 3.696271

Evaluate

m^{3} \times 200 - 10100

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

m^{3} \times 200 - 10100 = 0

Use the commutative property to reorder the terms

200 m^{3} - 10100 = 0

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

200 m^{3} = 0 + 10100

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

200 m^{3} = 10100

Divide both sides

\frac{200 m ^{3}}{200} = \frac{10100}{200}

Divide the numbers

m^{3} = \frac{10100}{200}

Cancel out the common factor 100

m^{3} = \frac{101}{2}

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

3 m^{3} = 3 \frac{101}{2}

Calculate

m = 3 \frac{101}{2}

Solution

More Steps

Evaluate

3 \frac{101}{2}

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

\frac{3 101}{3 2}

Multiply by the Conjugate

\frac{3 101 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 101 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3101 \times 34

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

3 101 \times 4

Calculate the product

3404

\frac{3 404}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 404}{2}

m = \frac{3 404}{2}

Alternative Form

m \approx 3.696271

Show Solution