Solve l^23184-1 - ScanMath

Question

Simplify the expression

3184 l^{2} - 1

Evaluate

l^{2} \times 3184 - 1

Solution

3184 l^{2} - 1

Show Solution

l_{1} = - \frac{199}{796}, l_{2} = \frac{199}{796}

Alternative Form

l_{1} \approx - 0.017722, l_{2} \approx 0.017722

Evaluate

l^{2} \times 3184 - 1

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

l^{2} \times 3184 - 1 = 0

Use the commutative property to reorder the terms

3184 l^{2} - 1 = 0

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

3184 l^{2} = 0 + 1

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

3184 l^{2} = 1

Divide both sides

\frac{3184 l ^{2}}{3184} = \frac{1}{3184}

Divide the numbers

l^{2} = \frac{1}{3184}

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

l = \pm \frac{1}{3184}

Simplify the expression

More Steps

Evaluate

\frac{1}{3184}

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

\frac{1}{3184}

Simplify the radical expression

\frac{1}{3184}

Simplify the radical expression

More Steps

Evaluate

3184

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

16 \times 199

Write the number in exponential form with the base of 4

4^{2} \times 199

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

4^{2} \times 199

Reduce the index of the radical and exponent with 2

4199

\frac{1}{4 199}

Multiply by the Conjugate

\frac{199}{4 199 \times 199}

Multiply the numbers

More Steps

Evaluate

4199 \times 199

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

4 \times 199

Multiply the terms

796

\frac{199}{796}

l = \pm \frac{199}{796}

Separate the equation into 2 possible cases

l = \frac{199}{796} l = - \frac{199}{796}

Solution

l_{1} = - \frac{199}{796}, l_{2} = \frac{199}{796}

Alternative Form

l_{1} \approx - 0.017722, l_{2} \approx 0.017722

Show Solution