Solve d^533-5-200

Question

Simplify the expression

33 d^{5} - 205

Evaluate

d^{5} \times 33 - 5 - 200

Use the commutative property to reorder the terms

33 d^{5} - 5 - 200

Solution

33 d^{5} - 205

Show Solution

d = \frac{5 205 \times 3 3 ^{4}}{33}

Alternative Form

d \approx 1.440947

Evaluate

d^{5} \times 33 - 5 - 200

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

d^{5} \times 33 - 5 - 200 = 0

Use the commutative property to reorder the terms

33 d^{5} - 5 - 200 = 0

Subtract the numbers

33 d^{5} - 205 = 0

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

33 d^{5} = 0 + 205

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

33 d^{5} = 205

Divide both sides

\frac{33 d ^{5}}{33} = \frac{205}{33}

Divide the numbers

d^{5} = \frac{205}{33}

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

5 d^{5} = 5 \frac{205}{33}

Calculate

d = 5 \frac{205}{33}

Solution

More Steps

Evaluate

5 \frac{205}{33}

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

\frac{5 205}{5 33}

Multiply by the Conjugate

\frac{5 205 \times 5 3 3 ^{4}}{5 33 \times 5 3 3 ^{4}}

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

\frac{5 205 \times 3 3 ^{4}}{5 33 \times 5 3 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

533 \times 5 3 3^{4}

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

5 33 \times 3 3^{4}

Calculate the product

5 3 3^{5}

Reduce the index of the radical and exponent with 5

33

\frac{5 205 \times 3 3 ^{4}}{33}

d = \frac{5 205 \times 3 3 ^{4}}{33}

Alternative Form

d \approx 1.440947

Show Solution