Solve d^533-5-205

Question

Simplify the expression

33 d^{5} - 210

Evaluate

d^{5} \times 33 - 5 - 205

Use the commutative property to reorder the terms

33 d^{5} - 5 - 205

Solution

33 d^{5} - 210

Show Solution

3 (11 d^{5} - 70)

Evaluate

d^{5} \times 33 - 5 - 205

Use the commutative property to reorder the terms

33 d^{5} - 5 - 205

Subtract the numbers

33 d^{5} - 210

Solution

3 (11 d^{5} - 70)

Show Solution

d = \frac{5 1024870}{11}

Alternative Form

d \approx 1.447908

Evaluate

d^{5} \times 33 - 5 - 205

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

d^{5} \times 33 - 5 - 205 = 0

Use the commutative property to reorder the terms

33 d^{5} - 5 - 205 = 0

Subtract the numbers

33 d^{5} - 210 = 0

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

33 d^{5} = 0 + 210

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

33 d^{5} = 210

Divide both sides

\frac{33 d ^{5}}{33} = \frac{210}{33}

Divide the numbers

d^{5} = \frac{210}{33}

Cancel out the common factor 3

d^{5} = \frac{70}{11}

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

5 d^{5} = 5 \frac{70}{11}

Calculate

d = 5 \frac{70}{11}

Solution

More Steps

Evaluate

5 \frac{70}{11}

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

\frac{5 70}{5 11}

Multiply by the Conjugate

\frac{5 70 \times 5 1 1 ^{4}}{5 11 \times 5 1 1 ^{4}}

Simplify

\frac{5 70 \times 5 14641}{5 11 \times 5 1 1 ^{4}}

Multiply the numbers

More Steps

Evaluate

570 \times 514641

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

5 70 \times 14641

Calculate the product

51024870

\frac{5 1024870}{5 11 \times 5 1 1 ^{4}}

Multiply the numbers

More Steps

Evaluate

511 \times 5 1 1^{4}

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

5 11 \times 1 1^{4}

Calculate the product

5 1 1^{5}

Reduce the index of the radical and exponent with 5

11

\frac{5 1024870}{11}

d = \frac{5 1024870}{11}

Alternative Form

d \approx 1.447908

Show Solution