Solve sigma^506-68-3

Question

Simplify the expression

6 σ^{5} - 71

Evaluate

σ^{5} \times 6 - 68 - 3

Use the commutative property to reorder the terms

6 σ^{5} - 68 - 3

Solution

6 σ^{5} - 71

Show Solution

σ = \frac{5 92016}{6}

Alternative Form

σ \approx 1.63916

Evaluate

σ^{5} \times 6 - 68 - 3

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

σ^{5} \times 6 - 68 - 3 = 0

Use the commutative property to reorder the terms

6 σ^{5} - 68 - 3 = 0

Subtract the numbers

6 σ^{5} - 71 = 0

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

6 σ^{5} = 0 + 71

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

6 σ^{5} = 71

Divide both sides

\frac{6 σ ^{5}}{6} = \frac{71}{6}

Divide the numbers

σ^{5} = \frac{71}{6}

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

5 σ^{5} = 5 \frac{71}{6}

Calculate

σ = 5 \frac{71}{6}

Solution

More Steps

Evaluate

5 \frac{71}{6}

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

\frac{5 71}{5 6}

Multiply by the Conjugate

\frac{5 71 \times 5 6 ^{4}}{5 6 \times 5 6 ^{4}}

Simplify

\frac{5 71 \times 5 1296}{5 6 \times 5 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

571 \times 51296

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

5 71 \times 1296

Calculate the product

592016

\frac{5 92016}{5 6 \times 5 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

56 \times 5 6^{4}

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

5 6 \times 6^{4}

Calculate the product

5 6^{5}

Reduce the index of the radical and exponent with 5

6

\frac{5 92016}{6}

σ = \frac{5 92016}{6}

Alternative Form

σ \approx 1.63916

Show Solution