Solve l^2242-9 - ScanMath

Question

Simplify the expression

242 l^{2} - 9

Evaluate

l^{2} \times 242 - 9

Solution

242 l^{2} - 9

Show Solution

l_{1} = - \frac{3 2}{22}, l_{2} = \frac{3 2}{22}

Alternative Form

l_{1} \approx - 0.192847, l_{2} \approx 0.192847

Evaluate

l^{2} \times 242 - 9

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

l^{2} \times 242 - 9 = 0

Use the commutative property to reorder the terms

242 l^{2} - 9 = 0

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

242 l^{2} = 0 + 9

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

242 l^{2} = 9

Divide both sides

\frac{242 l ^{2}}{242} = \frac{9}{242}

Divide the numbers

l^{2} = \frac{9}{242}

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

l = \pm \frac{9}{242}

Simplify the expression

More Steps

Evaluate

\frac{9}{242}

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

\frac{9}{242}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{242}

Simplify the radical expression

More Steps

Evaluate

242

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

121 \times 2

Write the number in exponential form with the base of 11

1 1^{2} \times 2

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

1 1^{2} \times 2

Reduce the index of the radical and exponent with 2

112

\frac{3}{11 2}

Multiply by the Conjugate

\frac{3 2}{11 2 \times 2}

Multiply the numbers

More Steps

Evaluate

112 \times 2

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

11 \times 2

Multiply the terms

22

\frac{3 2}{22}

l = \pm \frac{3 2}{22}

Separate the equation into 2 possible cases

l = \frac{3 2}{22} l = - \frac{3 2}{22}

Solution

l_{1} = - \frac{3 2}{22}, l_{2} = \frac{3 2}{22}

Alternative Form

l_{1} \approx - 0.192847, l_{2} \approx 0.192847

Show Solution