Solve 40s^5-15 - ScanMath

Question

Factor the expression

5 (8 s^{5} - 3)

Evaluate

40 s^{5} - 15

Solution

5 (8 s^{5} - 3)

Show Solution

s = \frac{5 12}{2}

Alternative Form

s \approx 0.821876

Evaluate

40 s^{5} - 15

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

40 s^{5} - 15 = 0

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

40 s^{5} = 0 + 15

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

40 s^{5} = 15

Divide both sides

\frac{40 s ^{5}}{40} = \frac{15}{40}

Divide the numbers

s^{5} = \frac{15}{40}

Cancel out the common factor 5

s^{5} = \frac{3}{8}

Take the 5 -th root on both sides of the equation

5 s^{5} = 5 \frac{3}{8}

Calculate

s = 5 \frac{3}{8}

Solution

More Steps

Evaluate

5 \frac{3}{8}

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

\frac{5 3}{5 8}

Multiply by the Conjugate

\frac{5 3 \times 5 8 ^{4}}{5 8 \times 5 8 ^{4}}

Simplify

\frac{5 3 \times 2 ^{2} 5 4}{5 8 \times 5 8 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 2^{2} 54

Multiply the terms

512 \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 512

\frac{2 ^{2} 5 12}{5 8 \times 5 8 ^{4}}

Multiply the numbers

More Steps

Evaluate

58 \times 5 8^{4}

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

5 8 \times 8^{4}

Calculate the product

5 8^{5}

Transform the expression

5 2^{15}

Reduce the index of the radical and exponent with 5

2^{3}

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

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{5 12}{2}

s = \frac{5 12}{2}

Alternative Form

s \approx 0.821876

Show Solution