Solve d^3243-8 - ScanMath

Question

Simplify the expression

243 d^{3} - 8

Evaluate

d^{3} \times 243 - 8

Solution

243 d^{3} - 8

Show Solution

d = \frac{2 3 3}{9}

Alternative Form

d \approx 0.3205

Evaluate

d^{3} \times 243 - 8

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

d^{3} \times 243 - 8 = 0

Use the commutative property to reorder the terms

243 d^{3} - 8 = 0

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

243 d^{3} = 0 + 8

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

243 d^{3} = 8

Divide both sides

\frac{243 d ^{3}}{243} = \frac{8}{243}

Divide the numbers

d^{3} = \frac{8}{243}

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

3 d^{3} = 3 \frac{8}{243}

Calculate

d = 3 \frac{8}{243}

Simplify the root

More Steps

Evaluate

3 \frac{8}{243}

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

\frac{3 8}{3 243}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{3 243}

Simplify the radical expression

More Steps

Evaluate

3243

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

3 27 \times 9

Write the number in exponential form with the base of 3

3 3^{3} \times 9

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

3 3^{3} \times 39

Reduce the index of the radical and exponent with 3

339

\frac{2}{3 3 9}

Multiply by the Conjugate

\frac{2 3 9 ^{2}}{3 3 9 \times 3 9 ^{2}}

Simplify

\frac{2 \times 3 3 3}{3 3 9 \times 3 9 ^{2}}

Multiply the numbers

\frac{6 3 3}{3 3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

339 \times 3 9^{2}

Multiply the terms

3 \times 3^{2}

Calculate the product

3^{3}

\frac{6 3 3}{3 ^{3}}

Rewrite the expression

\frac{3 \times 2 3 3}{3 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{3}{3 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{3 ^{3 - 1}}

Subtract the terms

\frac{1}{3 ^{2}}

\frac{2 3 3}{3 ^{2}}

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

Solution

d = \frac{2 3 3}{9}

Alternative Form

d \approx 0.3205

Show Solution