Solve 13=8v^3(v 8) - Socratic AI (ScanMath)

Question

Solve the equation

v_{1} = - \frac{4 52}{4}, v_{2} = \frac{4 52}{4}

Alternative Form

v_{1} \approx - 0.671337, v_{2} \approx 0.671337

Evaluate

13 = 8 v^{3} (v \times 8)

Remove the parentheses

13 = 8 v^{3} \times v \times 8

Multiply

More Steps

Evaluate

8 v^{3} \times v \times 8

Multiply the terms

64 v^{3} \times v

Multiply the terms with the same base by adding their exponents

64 v^{3 + 1}

Add the numbers

64 v^{4}

13 = 64 v^{4}

Swap the sides of the equation

64 v^{4} = 13

Divide both sides

\frac{64 v ^{4}}{64} = \frac{13}{64}

Divide the numbers

v^{4} = \frac{13}{64}

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm 4 \frac{13}{64}

Simplify the expression

More Steps

Evaluate

4 \frac{13}{64}

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

\frac{4 13}{4 64}

Simplify the radical expression

More Steps

Evaluate

464

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

4 16 \times 4

Write the number in exponential form with the base of 2

4 2^{4} \times 4

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

4 2^{4} \times 44

Reduce the index of the radical and exponent with 4

244

Simplify the root

22

\frac{4 13}{2 2}

Multiply by the Conjugate

\frac{4 13 \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

413 \times 2

Use n a = mn a^{m} to expand the expression

413 \times 4 2^{2}

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

4 13 \times 2^{2}

Calculate the product

452

\frac{4 52}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 2

Multiply the numbers

4

\frac{4 52}{4}

v = \pm \frac{4 52}{4}

Separate the equation into 2 possible cases

v = \frac{4 52}{4} v = - \frac{4 52}{4}

Solution

v_{1} = - \frac{4 52}{4}, v_{2} = \frac{4 52}{4}

Alternative Form

v_{1} \approx - 0.671337, v_{2} \approx 0.671337

Show Solution