Solve r^512-46-25

Question

Simplify the expression

12 r^{5} - 71

Evaluate

r^{5} \times 12 - 46 - 25

Use the commutative property to reorder the terms

12 r^{5} - 46 - 25

Solution

12 r^{5} - 71

Show Solution

r = \frac{5 46008}{6}

Alternative Form

r \approx 1.426972

Evaluate

r^{5} \times 12 - 46 - 25

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

r^{5} \times 12 - 46 - 25 = 0

Use the commutative property to reorder the terms

12 r^{5} - 46 - 25 = 0

Subtract the numbers

12 r^{5} - 71 = 0

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

12 r^{5} = 0 + 71

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

12 r^{5} = 71

Divide both sides

\frac{12 r ^{5}}{12} = \frac{71}{12}

Divide the numbers

r^{5} = \frac{71}{12}

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

5 r^{5} = 5 \frac{71}{12}

Calculate

r = 5 \frac{71}{12}

Solution

More Steps

Evaluate

5 \frac{71}{12}

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

\frac{5 71}{5 12}

Multiply by the Conjugate

\frac{5 71 \times 5 1 2 ^{4}}{5 12 \times 5 1 2 ^{4}}

Simplify

\frac{5 71 \times 2 5 648}{5 12 \times 5 1 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

571 \times 25648

Multiply the terms

546008 \times 2

Use the commutative property to reorder the terms

2546008

\frac{2 5 46008}{5 12 \times 5 1 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

512 \times 5 1 2^{4}

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

5 12 \times 1 2^{4}

Calculate the product

5 1 2^{5}

Reduce the index of the radical and exponent with 5

12

\frac{2 5 46008}{12}

Cancel out the common factor 2

\frac{5 46008}{6}

r = \frac{5 46008}{6}

Alternative Form

r \approx 1.426972

Show Solution