Solve m^39029/5-117 - Socratic AI (ScanMath)

Question

Simplify the expression

\frac{9029}{5} m^{3} - 117

Evaluate

m^{3} \times \frac{9029}{5} - 117

Solution

\frac{9029}{5} m^{3} - 117

Show Solution

\frac{1}{5} (9029 m^{3} - 585)

Evaluate

m^{3} \times \frac{9029}{5} - 117

Use the commutative property to reorder the terms

\frac{9029}{5} m^{3} - 117

Solution

\frac{1}{5} (9029 m^{3} - 585)

Show Solution

m = \frac{3 585 \times 902 9 ^{2}}{9029}

Alternative Form

m \approx 0.401642

Evaluate

m^{3} \times \frac{9029}{5} - 117

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

m^{3} \times \frac{9029}{5} - 117 = 0

Use the commutative property to reorder the terms

\frac{9029}{5} m^{3} - 117 = 0

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

\frac{9029}{5} m^{3} = 0 + 117

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

\frac{9029}{5} m^{3} = 117

Multiply by the reciprocal

\frac{9029}{5} m^{3} \times \frac{5}{9029} = 117 \times \frac{5}{9029}

Multiply

m^{3} = 117 \times \frac{5}{9029}

Multiply

More Steps

Evaluate

117 \times \frac{5}{9029}

Multiply the numbers

\frac{117 \times 5}{9029}

Multiply the numbers

\frac{585}{9029}

m^{3} = \frac{585}{9029}

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

3 m^{3} = 3 \frac{585}{9029}

Calculate

m = 3 \frac{585}{9029}

Solution

More Steps

Evaluate

3 \frac{585}{9029}

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

\frac{3 585}{3 9029}

Multiply by the Conjugate

\frac{3 585 \times 3 902 9 ^{2}}{3 9029 \times 3 902 9 ^{2}}

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

\frac{3 585 \times 902 9 ^{2}}{3 9029 \times 3 902 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39029 \times 3 902 9^{2}

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

3 9029 \times 902 9^{2}

Calculate the product

3 902 9^{3}

Reduce the index of the radical and exponent with 3

9029

\frac{3 585 \times 902 9 ^{2}}{9029}

m = \frac{3 585 \times 902 9 ^{2}}{9029}

Alternative Form

m \approx 0.401642

Show Solution