Solve 4b^211b-20 - ScanMath

Question

Simplify the expression

44 b^{3} - 20

Evaluate

4 b^{2} \times 11 b - 20

Solution

More Steps

Evaluate

4 b^{2} \times 11 b

Multiply the terms

44 b^{2} \times b

Multiply the terms with the same base by adding their exponents

44 b^{2 + 1}

Add the numbers

44 b^{3}

44 b^{3} - 20

Show Solution

Factor the expression

4 (11 b^{3} - 5)

Evaluate

4 b^{2} \times 11 b - 20

Multiply

More Steps

Evaluate

4 b^{2} \times 11 b

Multiply the terms

44 b^{2} \times b

Multiply the terms with the same base by adding their exponents

44 b^{2 + 1}

Add the numbers

44 b^{3}

44 b^{3} - 20

Solution

4 (11 b^{3} - 5)

Show Solution

Find the roots

b = \frac{3 605}{11}

Alternative Form

b \approx 0.768881

Evaluate

4 b^{2} \times 11 b - 20

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

4 b^{2} \times 11 b - 20 = 0

Multiply

More Steps

Multiply the terms

4 b^{2} \times 11 b

Multiply the terms

44 b^{2} \times b

Multiply the terms with the same base by adding their exponents

44 b^{2 + 1}

Add the numbers

44 b^{3}

44 b^{3} - 20 = 0

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

44 b^{3} = 0 + 20

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

44 b^{3} = 20

Divide both sides

\frac{44 b ^{3}}{44} = \frac{20}{44}

Divide the numbers

b^{3} = \frac{20}{44}

Cancel out the common factor 4

b^{3} = \frac{5}{11}

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

3 b^{3} = 3 \frac{5}{11}

Calculate

b = 3 \frac{5}{11}

Solution

More Steps

Evaluate

3 \frac{5}{11}

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

\frac{3 5}{3 11}

Multiply by the Conjugate

\frac{3 5 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{3 5 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3121

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

3 5 \times 121

Calculate the product

3605

\frac{3 605}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3 1 1^{2}

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

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{3 605}{11}

b = \frac{3 605}{11}

Alternative Form

b \approx 0.768881

Show Solution