Solve l^2212-1 - ScanMath

Question

Simplify the expression

212 l^{2} - 1

Evaluate

l^{2} \times 212 - 1

Solution

212 l^{2} - 1

Show Solution

l_{1} = - \frac{53}{106}, l_{2} = \frac{53}{106}

Alternative Form

l_{1} \approx - 0.06868, l_{2} \approx 0.06868

Evaluate

l^{2} \times 212 - 1

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

l^{2} \times 212 - 1 = 0

Use the commutative property to reorder the terms

212 l^{2} - 1 = 0

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

212 l^{2} = 0 + 1

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

212 l^{2} = 1

Divide both sides

\frac{212 l ^{2}}{212} = \frac{1}{212}

Divide the numbers

l^{2} = \frac{1}{212}

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

l = \pm \frac{1}{212}

Simplify the expression

More Steps

Evaluate

\frac{1}{212}

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

\frac{1}{212}

Simplify the radical expression

\frac{1}{212}

Simplify the radical expression

More Steps

Evaluate

212

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

4 \times 53

Write the number in exponential form with the base of 2

2^{2} \times 53

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

2^{2} \times 53

Reduce the index of the radical and exponent with 2

253

\frac{1}{2 53}

Multiply by the Conjugate

\frac{53}{2 53 \times 53}

Multiply the numbers

More Steps

Evaluate

253 \times 53

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

2 \times 53

Multiply the terms

106

\frac{53}{106}

l = \pm \frac{53}{106}

Separate the equation into 2 possible cases

l = \frac{53}{106} l = - \frac{53}{106}

Solution

l_{1} = - \frac{53}{106}, l_{2} = \frac{53}{106}

Alternative Form

l_{1} \approx - 0.06868, l_{2} \approx 0.06868

Show Solution