Solve 16b^(2) 60b-100

Question

Simplify the expression

960 b^{3} - 100

Evaluate

16 b^{2} \times 60 b - 100

Solution

More Steps

Evaluate

16 b^{2} \times 60 b

Multiply the terms

960 b^{2} \times b

Multiply the terms with the same base by adding their exponents

960 b^{2 + 1}

Add the numbers

960 b^{3}

960 b^{3} - 100

Show Solution

Factor the expression

20 (48 b^{3} - 5)

Evaluate

16 b^{2} \times 60 b - 100

Multiply

More Steps

Evaluate

16 b^{2} \times 60 b

Multiply the terms

960 b^{2} \times b

Multiply the terms with the same base by adding their exponents

960 b^{2 + 1}

Add the numbers

960 b^{3}

960 b^{3} - 100

Solution

20 (48 b^{3} - 5)

Show Solution

Find the roots

b = \frac{3 180}{12}

Alternative Form

b \approx 0.470518

Evaluate

16 b^{2} \times 60 b - 100

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

16 b^{2} \times 60 b - 100 = 0

Multiply

More Steps

Multiply the terms

16 b^{2} \times 60 b

Multiply the terms

960 b^{2} \times b

Multiply the terms with the same base by adding their exponents

960 b^{2 + 1}

Add the numbers

960 b^{3}

960 b^{3} - 100 = 0

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

960 b^{3} = 0 + 100

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

960 b^{3} = 100

Divide both sides

\frac{960 b ^{3}}{960} = \frac{100}{960}

Divide the numbers

b^{3} = \frac{100}{960}

Cancel out the common factor 20

b^{3} = \frac{5}{48}

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

3 b^{3} = 3 \frac{5}{48}

Calculate

b = 3 \frac{5}{48}

Solution

More Steps

Evaluate

3 \frac{5}{48}

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

\frac{3 5}{3 48}

Simplify the radical expression

More Steps

Evaluate

348

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

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

\frac{3 5}{2 3 6}

Multiply by the Conjugate

\frac{3 5 \times 3 6 ^{2}}{2 3 6 \times 3 6 ^{2}}

Simplify

\frac{3 5 \times 3 36}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 336

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

3 5 \times 36

Calculate the product

3180

\frac{3 180}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

236 \times 3 6^{2}

Multiply the terms

2 \times 6

Multiply the terms

12

\frac{3 180}{12}

b = \frac{3 180}{12}

Alternative Form

b \approx 0.470518

Show Solution