Solve dd^2225-3 - ScanMath

Question

Simplify the expression

225 d^{3} - 3

Evaluate

d \times d^{2} \times 225 - 3

Solution

More Steps

Evaluate

d \times d^{2} \times 225

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 225

Add the numbers

d^{3} \times 225

Use the commutative property to reorder the terms

225 d^{3}

225 d^{3} - 3

Show Solution

Factor the expression

3 (75 d^{3} - 1)

Evaluate

d \times d^{2} \times 225 - 3

Multiply

More Steps

Evaluate

d \times d^{2} \times 225

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 225

Add the numbers

d^{3} \times 225

Use the commutative property to reorder the terms

225 d^{3}

225 d^{3} - 3

Solution

3 (75 d^{3} - 1)

Show Solution

Find the roots

d = \frac{3 45}{15}

Alternative Form

d \approx 0.237126

Evaluate

d \times d^{2} \times 225 - 3

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

d \times d^{2} \times 225 - 3 = 0

Multiply

More Steps

Multiply the terms

d \times d^{2} \times 225

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 225

Add the numbers

d^{3} \times 225

Use the commutative property to reorder the terms

225 d^{3}

225 d^{3} - 3 = 0

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

225 d^{3} = 0 + 3

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

225 d^{3} = 3

Divide both sides

\frac{225 d ^{3}}{225} = \frac{3}{225}

Divide the numbers

d^{3} = \frac{3}{225}

Cancel out the common factor 3

d^{3} = \frac{1}{75}

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

3 d^{3} = 3 \frac{1}{75}

Calculate

d = 3 \frac{1}{75}

Solution

More Steps

Evaluate

3 \frac{1}{75}

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

\frac{3 1}{3 75}

Simplify the radical expression

\frac{1}{3 75}

Multiply by the Conjugate

\frac{3 7 5 ^{2}}{3 75 \times 3 7 5 ^{2}}

Simplify

\frac{5 3 45}{3 75 \times 3 7 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

375 \times 3 7 5^{2}

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

3 75 \times 7 5^{2}

Calculate the product

3 7 5^{3}

Reduce the index of the radical and exponent with 3

75

\frac{5 3 45}{75}

Cancel out the common factor 5

\frac{3 45}{15}

d = \frac{3 45}{15}

Alternative Form

d \approx 0.237126

Show Solution