Solve eta^2512-1 - ScanMath

Question

Simplify the expression

512 η^{2} - 1

Evaluate

η^{2} \times 512 - 1

Solution

512 η^{2} - 1

Show Solution

η_{1} = - \frac{2}{32}, η_{2} = \frac{2}{32}

Alternative Form

η_{1} \approx - 0.044194, η_{2} \approx 0.044194

Evaluate

η^{2} \times 512 - 1

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

η^{2} \times 512 - 1 = 0

Use the commutative property to reorder the terms

512 η^{2} - 1 = 0

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

512 η^{2} = 0 + 1

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

512 η^{2} = 1

Divide both sides

\frac{512 η ^{2}}{512} = \frac{1}{512}

Divide the numbers

η^{2} = \frac{1}{512}

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

η = \pm \frac{1}{512}

Simplify the expression

More Steps

Evaluate

\frac{1}{512}

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

\frac{1}{512}

Simplify the radical expression

\frac{1}{512}

Simplify the radical expression

More Steps

Evaluate

512

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

256 \times 2

Write the number in exponential form with the base of 16

1 6^{2} \times 2

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

1 6^{2} \times 2

Reduce the index of the radical and exponent with 2

162

\frac{1}{16 2}

Multiply by the Conjugate

\frac{2}{16 2 \times 2}

Multiply the numbers

More Steps

Evaluate

162 \times 2

When a square root of an expression is multiplied by itself,the result is that expression

16 \times 2

Multiply the terms

32

\frac{2}{32}

η = \pm \frac{2}{32}

Separate the equation into 2 possible cases

η = \frac{2}{32} η = - \frac{2}{32}

Solution

η_{1} = - \frac{2}{32}, η_{2} = \frac{2}{32}

Alternative Form

η_{1} \approx - 0.044194, η_{2} \approx 0.044194

Show Solution