Solve dd^2656-6 - ScanMath

Question

Simplify the expression

656 d^{3} - 6

Evaluate

d \times d^{2} \times 656 - 6

Solution

More Steps

Evaluate

d \times d^{2} \times 656

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 656

Add the numbers

d^{3} \times 656

Use the commutative property to reorder the terms

656 d^{3}

656 d^{3} - 6

Show Solution

Factor the expression

2 (328 d^{3} - 3)

Evaluate

d \times d^{2} \times 656 - 6

Multiply

More Steps

Evaluate

d \times d^{2} \times 656

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 656

Add the numbers

d^{3} \times 656

Use the commutative property to reorder the terms

656 d^{3}

656 d^{3} - 6

Solution

2 (328 d^{3} - 3)

Show Solution

Find the roots

d = \frac{3 5043}{82}

Alternative Form

d \approx 0.20913

Evaluate

d \times d^{2} \times 656 - 6

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

d \times d^{2} \times 656 - 6 = 0

Multiply

More Steps

Multiply the terms

d \times d^{2} \times 656

Multiply the terms with the same base by adding their exponents

d^{1 + 2} \times 656

Add the numbers

d^{3} \times 656

Use the commutative property to reorder the terms

656 d^{3}

656 d^{3} - 6 = 0

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

656 d^{3} = 0 + 6

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

656 d^{3} = 6

Divide both sides

\frac{656 d ^{3}}{656} = \frac{6}{656}

Divide the numbers

d^{3} = \frac{6}{656}

Cancel out the common factor 2

d^{3} = \frac{3}{328}

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

3 d^{3} = 3 \frac{3}{328}

Calculate

d = 3 \frac{3}{328}

Solution

More Steps

Evaluate

3 \frac{3}{328}

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

\frac{3 3}{3 328}

Simplify the radical expression

More Steps

Evaluate

3328

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 41

Write the number in exponential form with the base of 2

3 2^{3} \times 41

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 341

Reduce the index of the radical and exponent with 3

2341

\frac{3 3}{2 3 41}

Multiply by the Conjugate

\frac{3 3 \times 3 4 1 ^{2}}{2 3 41 \times 3 4 1 ^{2}}

Simplify

\frac{3 3 \times 3 1681}{2 3 41 \times 3 4 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 31681

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

3 3 \times 1681

Calculate the product

35043

\frac{3 5043}{2 3 41 \times 3 4 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

2341 \times 3 4 1^{2}

Multiply the terms

2 \times 41

Multiply the terms

82

\frac{3 5043}{82}

d = \frac{3 5043}{82}

Alternative Form

d \approx 0.20913

Show Solution