Solve 5r^214r-24 - ScanMath

Question

Simplify the expression

70 r^{3} - 24

Evaluate

5 r^{2} \times 14 r - 24

Solution

More Steps

Evaluate

5 r^{2} \times 14 r

Multiply the terms

70 r^{2} \times r

Multiply the terms with the same base by adding their exponents

70 r^{2 + 1}

Add the numbers

70 r^{3}

70 r^{3} - 24

Show Solution

Factor the expression

2 (35 r^{3} - 12)

Evaluate

5 r^{2} \times 14 r - 24

Multiply

More Steps

Evaluate

5 r^{2} \times 14 r

Multiply the terms

70 r^{2} \times r

Multiply the terms with the same base by adding their exponents

70 r^{2 + 1}

Add the numbers

70 r^{3}

70 r^{3} - 24

Solution

2 (35 r^{3} - 12)

Show Solution

Find the roots

r = \frac{3 14700}{35}

Alternative Form

r \approx 0.699903

Evaluate

5 r^{2} \times 14 r - 24

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

5 r^{2} \times 14 r - 24 = 0

Multiply

More Steps

Multiply the terms

5 r^{2} \times 14 r

Multiply the terms

70 r^{2} \times r

Multiply the terms with the same base by adding their exponents

70 r^{2 + 1}

Add the numbers

70 r^{3}

70 r^{3} - 24 = 0

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

70 r^{3} = 0 + 24

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

70 r^{3} = 24

Divide both sides

\frac{70 r ^{3}}{70} = \frac{24}{70}

Divide the numbers

r^{3} = \frac{24}{70}

Cancel out the common factor 2

r^{3} = \frac{12}{35}

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

3 r^{3} = 3 \frac{12}{35}

Calculate

r = 3 \frac{12}{35}

Solution

More Steps

Evaluate

3 \frac{12}{35}

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

\frac{3 12}{3 35}

Multiply by the Conjugate

\frac{3 12 \times 3 3 5 ^{2}}{3 35 \times 3 3 5 ^{2}}

Simplify

\frac{3 12 \times 3 1225}{3 35 \times 3 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 31225

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

3 12 \times 1225

Calculate the product

314700

\frac{3 14700}{3 35 \times 3 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

335 \times 3 3 5^{2}

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

3 35 \times 3 5^{2}

Calculate the product

3 3 5^{3}

Reduce the index of the radical and exponent with 3

35

\frac{3 14700}{35}

r = \frac{3 14700}{35}

Alternative Form

r \approx 0.699903

Show Solution