Solve D^54-4-17 - ScanMath

Question

Simplify the expression

4 D^{5} - 21

Evaluate

D^{5} \times 4 - 4 - 17

Use the commutative property to reorder the terms

4 D^{5} - 4 - 17

Solution

4 D^{5} - 21

Show Solution

D = \frac{5 168}{2}

Alternative Form

D \approx 1.393259

Evaluate

D^{5} \times 4 - 4 - 17

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

D^{5} \times 4 - 4 - 17 = 0

Use the commutative property to reorder the terms

4 D^{5} - 4 - 17 = 0

Subtract the numbers

4 D^{5} - 21 = 0

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

4 D^{5} = 0 + 21

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

4 D^{5} = 21

Divide both sides

\frac{4 D ^{5}}{4} = \frac{21}{4}

Divide the numbers

D^{5} = \frac{21}{4}

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

5 D^{5} = 5 \frac{21}{4}

Calculate

D = 5 \frac{21}{4}

Solution

More Steps

Evaluate

5 \frac{21}{4}

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

\frac{5 21}{5 4}

Multiply by the Conjugate

\frac{5 21 \times 5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{5 21 \times 2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

521 \times 258

Multiply the terms

5168 \times 2

Use the commutative property to reorder the terms

25168

\frac{2 5 168}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

54 \times 5 4^{4}

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

5 4 \times 4^{4}

Calculate the product

5 4^{5}

Transform the expression

5 2^{10}

Reduce the index of the radical and exponent with 5

2^{2}

\frac{2 5 168}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

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

Simplify

\frac{1}{2}

\frac{5 168}{2}

D = \frac{5 168}{2}

Alternative Form

D \approx 1.393259

Show Solution