Solve dd^2224-200

Question

Simplify the expression

224 d^{3} - 200

Evaluate

d \times d^{2} \times 224 - 200

Solution

More Steps

Evaluate

d \times d^{2} \times 224

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 224

Add the numbers

d^{3} \times 224

Use the commutative property to reorder the terms

224 d^{3}

224 d^{3} - 200

Show Solution

Factor the expression

8 (28 d^{3} - 25)

Evaluate

d \times d^{2} \times 224 - 200

Multiply

More Steps

Evaluate

d \times d^{2} \times 224

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 224

Add the numbers

d^{3} \times 224

Use the commutative property to reorder the terms

224 d^{3}

224 d^{3} - 200

Solution

8 (28 d^{3} - 25)

Show Solution

Find the roots

d = \frac{3 2450}{14}

Alternative Form

d \approx 0.962928

Evaluate

d \times d^{2} \times 224 - 200

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

d \times d^{2} \times 224 - 200 = 0

Multiply

More Steps

Multiply the terms

d \times d^{2} \times 224

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 224

Add the numbers

d^{3} \times 224

Use the commutative property to reorder the terms

224 d^{3}

224 d^{3} - 200 = 0

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

224 d^{3} = 0 + 200

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

224 d^{3} = 200

Divide both sides

\frac{224 d ^{3}}{224} = \frac{200}{224}

Divide the numbers

d^{3} = \frac{200}{224}

Cancel out the common factor 8

d^{3} = \frac{25}{28}

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

3 d^{3} = 3 \frac{25}{28}

Calculate

d = 3 \frac{25}{28}

Solution

More Steps

Evaluate

3 \frac{25}{28}

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

\frac{3 25}{3 28}

Multiply by the Conjugate

\frac{3 25 \times 3 2 8 ^{2}}{3 28 \times 3 2 8 ^{2}}

Simplify

\frac{3 25 \times 2 3 98}{3 28 \times 3 2 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

325 \times 2398

Multiply the terms

32450 \times 2

Use the commutative property to reorder the terms

232450

\frac{2 3 2450}{3 28 \times 3 2 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

328 \times 3 2 8^{2}

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

3 28 \times 2 8^{2}

Calculate the product

3 2 8^{3}

Reduce the index of the radical and exponent with 3

28

\frac{2 3 2450}{28}

Cancel out the common factor 2

\frac{3 2450}{14}

d = \frac{3 2450}{14}

Alternative Form

d \approx 0.962928

Show Solution