Solve r^590-190-11

Question

Simplify the expression

90 r^{5} - 201

Evaluate

r^{5} \times 90 - 190 - 11

Use the commutative property to reorder the terms

90 r^{5} - 190 - 11

Solution

90 r^{5} - 201

Show Solution

3 (30 r^{5} - 67)

Evaluate

r^{5} \times 90 - 190 - 11

Use the commutative property to reorder the terms

90 r^{5} - 190 - 11

Subtract the numbers

90 r^{5} - 201

Solution

3 (30 r^{5} - 67)

Show Solution

r = \frac{5 67 \times 3 0 ^{4}}{30}

Alternative Form

r \approx 1.174331

Evaluate

r^{5} \times 90 - 190 - 11

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

r^{5} \times 90 - 190 - 11 = 0

Use the commutative property to reorder the terms

90 r^{5} - 190 - 11 = 0

Subtract the numbers

90 r^{5} - 201 = 0

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

90 r^{5} = 0 + 201

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

90 r^{5} = 201

Divide both sides

\frac{90 r ^{5}}{90} = \frac{201}{90}

Divide the numbers

r^{5} = \frac{201}{90}

Cancel out the common factor 3

r^{5} = \frac{67}{30}

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

5 r^{5} = 5 \frac{67}{30}

Calculate

r = 5 \frac{67}{30}

Solution

More Steps

Evaluate

5 \frac{67}{30}

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

\frac{5 67}{5 30}

Multiply by the Conjugate

\frac{5 67 \times 5 3 0 ^{4}}{5 30 \times 5 3 0 ^{4}}

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

\frac{5 67 \times 3 0 ^{4}}{5 30 \times 5 3 0 ^{4}}

Multiply the numbers

More Steps

Evaluate

530 \times 5 3 0^{4}

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

5 30 \times 3 0^{4}

Calculate the product

5 3 0^{5}

Reduce the index of the radical and exponent with 5

30

\frac{5 67 \times 3 0 ^{4}}{30}

r = \frac{5 67 \times 3 0 ^{4}}{30}

Alternative Form

r \approx 1.174331

Show Solution