Solve r^2 8r-20 - ScanMath

Question

Simplify the expression

8 r^{3} - 20

Evaluate

r^{2} \times 8 r - 20

Solution

More Steps

Evaluate

r^{2} \times 8 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 8

Add the numbers

r^{3} \times 8

Use the commutative property to reorder the terms

8 r^{3}

8 r^{3} - 20

Show Solution

Factor the expression

4 (2 r^{3} - 5)

Evaluate

r^{2} \times 8 r - 20

Multiply

More Steps

Evaluate

r^{2} \times 8 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 8

Add the numbers

r^{3} \times 8

Use the commutative property to reorder the terms

8 r^{3}

8 r^{3} - 20

Solution

4 (2 r^{3} - 5)

Show Solution

Find the roots

r = \frac{3 20}{2}

Alternative Form

r \approx 1.357209

Evaluate

r^{2} \times 8 r - 20

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

r^{2} \times 8 r - 20 = 0

Multiply

More Steps

Multiply the terms

r^{2} \times 8 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 8

Add the numbers

r^{3} \times 8

Use the commutative property to reorder the terms

8 r^{3}

8 r^{3} - 20 = 0

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

8 r^{3} = 0 + 20

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

8 r^{3} = 20

Divide both sides

\frac{8 r ^{3}}{8} = \frac{20}{8}

Divide the numbers

r^{3} = \frac{20}{8}

Cancel out the common factor 4

r^{3} = \frac{5}{2}

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

3 r^{3} = 3 \frac{5}{2}

Calculate

r = 3 \frac{5}{2}

Solution

More Steps

Evaluate

3 \frac{5}{2}

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

\frac{3 5}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 5 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 34

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

3 5 \times 4

Calculate the product

320

\frac{3 20}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 20}{2}

r = \frac{3 20}{2}

Alternative Form

r \approx 1.357209

Show Solution