Solve sigma^28-841984

Question

Simplify the expression

8 σ^{2} - 841984

Evaluate

σ^{2} \times 8 - 841984

Solution

8 σ^{2} - 841984

Show Solution

8 (σ^{2} - 105248)

Evaluate

σ^{2} \times 8 - 841984

Use the commutative property to reorder the terms

8 σ^{2} - 841984

Solution

8 (σ^{2} - 105248)

Show Solution

σ_{1} = - 46578, σ_{2} = 46578

Alternative Form

σ_{1} \approx - 324.419482, σ_{2} \approx 324.419482

Evaluate

σ^{2} \times 8 - 841984

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

σ^{2} \times 8 - 841984 = 0

Use the commutative property to reorder the terms

8 σ^{2} - 841984 = 0

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

8 σ^{2} = 0 + 841984

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

8 σ^{2} = 841984

Divide both sides

\frac{8 σ ^{2}}{8} = \frac{841984}{8}

Divide the numbers

σ^{2} = \frac{841984}{8}

Divide the numbers

More Steps

Evaluate

\frac{841984}{8}

Reduce the numbers

\frac{105248}{1}

Calculate

105248

σ^{2} = 105248

Take the root of both sides of the equation and remember to use both positive and negative roots

σ = \pm 105248

Simplify the expression

More Steps

Evaluate

105248

Write the expression as a product where the root of one of the factors can be evaluated

16 \times 6578

Write the number in exponential form with the base of 4

4^{2} \times 6578

The root of a product is equal to the product of the roots of each factor

4^{2} \times 6578

Reduce the index of the radical and exponent with 2

46578

σ = \pm 46578

Separate the equation into 2 possible cases

σ = 46578 σ = - 46578

Solution

σ_{1} = - 46578, σ_{2} = 46578

Alternative Form

σ_{1} \approx - 324.419482, σ_{2} \approx 324.419482

Show Solution