Solve r^2511 1/8-1/4

Question

Simplify the expression

\frac{4089}{8} r^{2} - \frac{1}{4}

Evaluate

r^{2} \times 511 \frac{1}{8} - \frac{1}{4}

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

511 \frac{1}{8}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{511 \times 8 + 1}{8}

Multiply the terms

\frac{4088 + 1}{8}

Add the terms

\frac{4089}{8}

r^{2} \times \frac{4089}{8} - \frac{1}{4}

Solution

\frac{4089}{8} r^{2} - \frac{1}{4}

Show Solution

Factor the expression

\frac{1}{8} (4089 r^{2} - 2)

Evaluate

r^{2} \times 511 \frac{1}{8} - \frac{1}{4}

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

511 \frac{1}{8}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{511 \times 8 + 1}{8}

Multiply the terms

\frac{4088 + 1}{8}

Add the terms

\frac{4089}{8}

r^{2} \times \frac{4089}{8} - \frac{1}{4}

Use the commutative property to reorder the terms

\frac{4089}{8} r^{2} - \frac{1}{4}

Solution

\frac{1}{8} (4089 r^{2} - 2)

Show Solution

Find the roots

r_{1} = - \frac{8178}{4089}, r_{2} = \frac{8178}{4089}

Alternative Form

r_{1} \approx - 0.022116, r_{2} \approx 0.022116

Evaluate

r^{2} \times 511 \frac{1}{8} - \frac{1}{4}

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

r^{2} \times 511 \frac{1}{8} - \frac{1}{4} = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

511 \frac{1}{8}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{511 \times 8 + 1}{8}

Multiply the terms

\frac{4088 + 1}{8}

Add the terms

\frac{4089}{8}

r^{2} \times \frac{4089}{8} - \frac{1}{4} = 0

Use the commutative property to reorder the terms

\frac{4089}{8} r^{2} - \frac{1}{4} = 0

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

\frac{4089}{8} r^{2} = 0 + \frac{1}{4}

Add the terms

\frac{4089}{8} r^{2} = \frac{1}{4}

Multiply by the reciprocal

\frac{4089}{8} r^{2} \times \frac{8}{4089} = \frac{1}{4} \times \frac{8}{4089}

Multiply

r^{2} = \frac{1}{4} \times \frac{8}{4089}

Multiply

More Steps

Evaluate

\frac{1}{4} \times \frac{8}{4089}

Reduce the numbers

1 \times \frac{2}{4089}

Multiply the numbers

\frac{2}{4089}

r^{2} = \frac{2}{4089}

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

r = \pm \frac{2}{4089}

Simplify the expression

More Steps

Evaluate

\frac{2}{4089}

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

\frac{2}{4089}

Multiply by the Conjugate

\frac{2 \times 4089}{4089 \times 4089}

Multiply the numbers

More Steps

Evaluate

2 \times 4089

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

2 \times 4089

Calculate the product

8178

\frac{8178}{4089 \times 4089}

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

\frac{8178}{4089}

r = \pm \frac{8178}{4089}

Separate the equation into 2 possible cases

r = \frac{8178}{4089} r = - \frac{8178}{4089}

Solution

r_{1} = - \frac{8178}{4089}, r_{2} = \frac{8178}{4089}

Alternative Form

r_{1} \approx - 0.022116, r_{2} \approx 0.022116

Show Solution