Solve dd^2968-100

Question

Simplify the expression

968 d^{3} - 100

Evaluate

d \times d^{2} \times 968 - 100

Solution

More Steps

Evaluate

d \times d^{2} \times 968

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 968

Add the numbers

d^{3} \times 968

Use the commutative property to reorder the terms

968 d^{3}

968 d^{3} - 100

Show Solution

Factor the expression

4 (242 d^{3} - 25)

Evaluate

d \times d^{2} \times 968 - 100

Multiply

More Steps

Evaluate

d \times d^{2} \times 968

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 968

Add the numbers

d^{3} \times 968

Use the commutative property to reorder the terms

968 d^{3}

968 d^{3} - 100

Solution

4 (242 d^{3} - 25)

Show Solution

Find the roots

d = \frac{3 1100}{22}

Alternative Form

d \approx 0.469218

Evaluate

d \times d^{2} \times 968 - 100

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

d \times d^{2} \times 968 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{2} \times 968

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 968

Add the numbers

d^{3} \times 968

Use the commutative property to reorder the terms

968 d^{3}

968 d^{3} - 100 = 0

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

968 d^{3} = 0 + 100

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

968 d^{3} = 100

Divide both sides

\frac{968 d ^{3}}{968} = \frac{100}{968}

Divide the numbers

d^{3} = \frac{100}{968}

Cancel out the common factor 4

d^{3} = \frac{25}{242}

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

3 d^{3} = 3 \frac{25}{242}

Calculate

d = 3 \frac{25}{242}

Solution

More Steps

Evaluate

3 \frac{25}{242}

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

\frac{3 25}{3 242}

Multiply by the Conjugate

\frac{3 25 \times 3 24 2 ^{2}}{3 242 \times 3 24 2 ^{2}}

Simplify

\frac{3 25 \times 11 3 44}{3 242 \times 3 24 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

325 \times 11344

Multiply the terms

31100 \times 11

Use the commutative property to reorder the terms

1131100

\frac{11 3 1100}{3 242 \times 3 24 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3242 \times 3 24 2^{2}

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

3 242 \times 24 2^{2}

Calculate the product

3 24 2^{3}

Reduce the index of the radical and exponent with 3

242

\frac{11 3 1100}{242}

Cancel out the common factor 11

\frac{3 1100}{22}

d = \frac{3 1100}{22}

Alternative Form

d \approx 0.469218

Show Solution