Solve 24a^34-27 - ScanMath

Question

Simplify the expression

96 a^{3} - 27

Evaluate

24 a^{3} \times 4 - 27

Solution

96 a^{3} - 27

Show Solution

3 (32 a^{3} - 9)

Evaluate

24 a^{3} \times 4 - 27

Multiply the terms

96 a^{3} - 27

Solution

3 (32 a^{3} - 9)

Show Solution

a = \frac{3 18}{4}

Alternative Form

a \approx 0.655185

Evaluate

24 a^{3} \times 4 - 27

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

24 a^{3} \times 4 - 27 = 0

Multiply the terms

96 a^{3} - 27 = 0

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

96 a^{3} = 0 + 27

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

96 a^{3} = 27

Divide both sides

\frac{96 a ^{3}}{96} = \frac{27}{96}

Divide the numbers

a^{3} = \frac{27}{96}

Cancel out the common factor 3

a^{3} = \frac{9}{32}

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

3 a^{3} = 3 \frac{9}{32}

Calculate

a = 3 \frac{9}{32}

Simplify the root

More Steps

Evaluate

3 \frac{9}{32}

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

\frac{3 9}{3 32}

Simplify the radical expression

More Steps

Evaluate

332

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

3 8 \times 4

Write the number in exponential form with the base of 2

3 2^{3} \times 4

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

3 2^{3} \times 34

Reduce the index of the radical and exponent with 3

234

\frac{3 9}{2 3 4}

Multiply by the Conjugate

\frac{3 9 \times 3 4 ^{2}}{2 3 4 \times 3 4 ^{2}}

Simplify

\frac{3 9 \times 2 3 2}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 232

Multiply the terms

318 \times 2

Use the commutative property to reorder the terms

2318

\frac{2 3 18}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

234 \times 3 4^{2}

Multiply the terms

2 \times 2^{2}

Calculate the product

2^{3}

\frac{2 3 18}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

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

\frac{3 18}{2 ^{2}}

a = \frac{3 18}{2 ^{2}}

Solution

a = \frac{3 18}{4}

Alternative Form

a \approx 0.655185

Show Solution