Solve l^282024-25

Question

Simplify the expression

82024 l^{2} - 25

Evaluate

l^{2} \times 82024 - 25

Solution

82024 l^{2} - 25

Show Solution

l_{1} = - \frac{5 20506}{41012}, l_{2} = \frac{5 20506}{41012}

Alternative Form

l_{1} \approx - 0.017458, l_{2} \approx 0.017458

Evaluate

l^{2} \times 82024 - 25

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

l^{2} \times 82024 - 25 = 0

Use the commutative property to reorder the terms

82024 l^{2} - 25 = 0

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

82024 l^{2} = 0 + 25

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

82024 l^{2} = 25

Divide both sides

\frac{82024 l ^{2}}{82024} = \frac{25}{82024}

Divide the numbers

l^{2} = \frac{25}{82024}

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

l = \pm \frac{25}{82024}

Simplify the expression

More Steps

Evaluate

\frac{25}{82024}

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

\frac{25}{82024}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{82024}

Simplify the radical expression

More Steps

Evaluate

82024

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

4 \times 20506

Write the number in exponential form with the base of 2

2^{2} \times 20506

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

2^{2} \times 20506

Reduce the index of the radical and exponent with 2

220506

\frac{5}{2 20506}

Multiply by the Conjugate

\frac{5 20506}{2 20506 \times 20506}

Multiply the numbers

More Steps

Evaluate

220506 \times 20506

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

2 \times 20506

Multiply the terms

41012

\frac{5 20506}{41012}

l = \pm \frac{5 20506}{41012}

Separate the equation into 2 possible cases

l = \frac{5 20506}{41012} l = - \frac{5 20506}{41012}

Solution

l_{1} = - \frac{5 20506}{41012}, l_{2} = \frac{5 20506}{41012}

Alternative Form

l_{1} \approx - 0.017458, l_{2} \approx 0.017458

Show Solution