Solve dd^2820-8 - ScanMath

Question

Simplify the expression

820 d^{3} - 8

Evaluate

d \times d^{2} \times 820 - 8

Solution

More Steps

Evaluate

d \times d^{2} \times 820

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 820

Add the numbers

d^{3} \times 820

Use the commutative property to reorder the terms

820 d^{3}

820 d^{3} - 8

Show Solution

Factor the expression

4 (205 d^{3} - 2)

Evaluate

d \times d^{2} \times 820 - 8

Multiply

More Steps

Evaluate

d \times d^{2} \times 820

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 820

Add the numbers

d^{3} \times 820

Use the commutative property to reorder the terms

820 d^{3}

820 d^{3} - 8

Solution

4 (205 d^{3} - 2)

Show Solution

Find the roots

d = \frac{3 84050}{205}

Alternative Form

d \approx 0.213677

Evaluate

d \times d^{2} \times 820 - 8

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

d \times d^{2} \times 820 - 8 = 0

Multiply

More Steps

Multiply the terms

d \times d^{2} \times 820

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 820

Add the numbers

d^{3} \times 820

Use the commutative property to reorder the terms

820 d^{3}

820 d^{3} - 8 = 0

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

820 d^{3} = 0 + 8

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

820 d^{3} = 8

Divide both sides

\frac{820 d ^{3}}{820} = \frac{8}{820}

Divide the numbers

d^{3} = \frac{8}{820}

Cancel out the common factor 4

d^{3} = \frac{2}{205}

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

3 d^{3} = 3 \frac{2}{205}

Calculate

d = 3 \frac{2}{205}

Solution

More Steps

Evaluate

3 \frac{2}{205}

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

\frac{3 2}{3 205}

Multiply by the Conjugate

\frac{3 2 \times 3 20 5 ^{2}}{3 205 \times 3 20 5 ^{2}}

Simplify

\frac{3 2 \times 3 42025}{3 205 \times 3 20 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 342025

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

3 2 \times 42025

Calculate the product

384050

\frac{3 84050}{3 205 \times 3 20 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

3205 \times 3 20 5^{2}

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

3 205 \times 20 5^{2}

Calculate the product

3 20 5^{3}

Reduce the index of the radical and exponent with 3

205

\frac{3 84050}{205}

d = \frac{3 84050}{205}

Alternative Form

d \approx 0.213677

Show Solution