Solve r^352-333-3333

Question

Simplify the expression

52 r^{3} - 3666

Evaluate

r^{3} \times 52 - 333 - 3333

Use the commutative property to reorder the terms

52 r^{3} - 333 - 3333

Solution

52 r^{3} - 3666

Show Solution

26 (2 r^{3} - 141)

Evaluate

r^{3} \times 52 - 333 - 3333

Use the commutative property to reorder the terms

52 r^{3} - 333 - 3333

Subtract the numbers

52 r^{3} - 3666

Solution

26 (2 r^{3} - 141)

Show Solution

r = \frac{3 564}{2}

Alternative Form

r \approx 4.131075

Evaluate

r^{3} \times 52 - 333 - 3333

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

r^{3} \times 52 - 333 - 3333 = 0

Use the commutative property to reorder the terms

52 r^{3} - 333 - 3333 = 0

Subtract the numbers

52 r^{3} - 3666 = 0

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

52 r^{3} = 0 + 3666

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

52 r^{3} = 3666

Divide both sides

\frac{52 r ^{3}}{52} = \frac{3666}{52}

Divide the numbers

r^{3} = \frac{3666}{52}

Cancel out the common factor 26

r^{3} = \frac{141}{2}

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

3 r^{3} = 3 \frac{141}{2}

Calculate

r = 3 \frac{141}{2}

Solution

More Steps

Evaluate

3 \frac{141}{2}

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

\frac{3 141}{3 2}

Multiply by the Conjugate

\frac{3 141 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 141 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3141 \times 34

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

3 141 \times 4

Calculate the product

3564

\frac{3 564}{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{3 564}{2}

r = \frac{3 564}{2}

Alternative Form

r \approx 4.131075

Show Solution