Solve 13-6(a^2) 8 a

Question

Simplify the expression

13 - 48 a^{3}

Evaluate

13 - 6 a^{2} \times 8 a

Solution

More Steps

Evaluate

6 a^{2} \times 8 a

Multiply the terms

48 a^{2} \times a

Multiply the terms with the same base by adding their exponents

48 a^{2 + 1}

Add the numbers

48 a^{3}

13 - 48 a^{3}

Show Solution

Find the roots

a = \frac{3 468}{12}

Alternative Form

a \approx 0.646995

Evaluate

13 - 6 (a^{2}) \times 8 a

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

13 - 6 (a^{2}) \times 8 a = 0

Calculate

13 - 6 a^{2} \times 8 a = 0

Multiply

More Steps

Multiply the terms

6 a^{2} \times 8 a

Multiply the terms

48 a^{2} \times a

Multiply the terms with the same base by adding their exponents

48 a^{2 + 1}

Add the numbers

48 a^{3}

13 - 48 a^{3} = 0

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

- 48 a^{3} = 0 - 13

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

- 48 a^{3} = - 13

Change the signs on both sides of the equation

48 a^{3} = 13

Divide both sides

\frac{48 a ^{3}}{48} = \frac{13}{48}

Divide the numbers

a^{3} = \frac{13}{48}

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

3 a^{3} = 3 \frac{13}{48}

Calculate

a = 3 \frac{13}{48}

Solution

More Steps

Evaluate

3 \frac{13}{48}

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

\frac{3 13}{3 48}

Simplify the radical expression

More Steps

Evaluate

348

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

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

\frac{3 13}{2 3 6}

Multiply by the Conjugate

\frac{3 13 \times 3 6 ^{2}}{2 3 6 \times 3 6 ^{2}}

Simplify

\frac{3 13 \times 3 36}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 336

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

3 13 \times 36

Calculate the product

3468

\frac{3 468}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

236 \times 3 6^{2}

Multiply the terms

2 \times 6

Multiply the terms

12

\frac{3 468}{12}

a = \frac{3 468}{12}

Alternative Form

a \approx 0.646995

Show Solution