Solve k^2 5k-24 - ScanMath

Question

Simplify the expression

5 k^{3} - 24

Evaluate

k^{2} \times 5 k - 24

Solution

More Steps

Evaluate

k^{2} \times 5 k

Multiply the terms with the same base by adding their exponents

k^{2 + 1} \times 5

Add the numbers

k^{3} \times 5

Use the commutative property to reorder the terms

5 k^{3}

5 k^{3} - 24

Show Solution

k = \frac{2 3 75}{5}

Alternative Form

k \approx 1.686865

Evaluate

k^{2} \times 5 k - 24

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

k^{2} \times 5 k - 24 = 0

Multiply

More Steps

Multiply the terms

k^{2} \times 5 k

Multiply the terms with the same base by adding their exponents

k^{2 + 1} \times 5

Add the numbers

k^{3} \times 5

Use the commutative property to reorder the terms

5 k^{3}

5 k^{3} - 24 = 0

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

5 k^{3} = 0 + 24

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

5 k^{3} = 24

Divide both sides

\frac{5 k ^{3}}{5} = \frac{24}{5}

Divide the numbers

k^{3} = \frac{24}{5}

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

3 k^{3} = 3 \frac{24}{5}

Calculate

k = 3 \frac{24}{5}

Solution

More Steps

Evaluate

3 \frac{24}{5}

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

\frac{3 24}{3 5}

Simplify the radical expression

More Steps

Evaluate

324

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

3 8 \times 3

Write the number in exponential form with the base of 2

3 2^{3} \times 3

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

3 2^{3} \times 33

Reduce the index of the radical and exponent with 3

233

\frac{2 3 3}{3 5}

Multiply by the Conjugate

\frac{2 3 3 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{2 3 3 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 325

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

3 3 \times 25

Calculate the product

375

\frac{2 3 75}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{2 3 75}{5}

k = \frac{2 3 75}{5}

Alternative Form

k \approx 1.686865

Show Solution