Solve L^24752-1 - ScanMath

Question

Simplify the expression

4752 L^{2} - 1

Evaluate

L^{2} \times 4752 - 1

Solution

4752 L^{2} - 1

Show Solution

L_{1} = - \frac{33}{396}, L_{2} = \frac{33}{396}

Alternative Form

L_{1} \approx - 0.014506, L_{2} \approx 0.014506

Evaluate

L^{2} \times 4752 - 1

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

L^{2} \times 4752 - 1 = 0

Use the commutative property to reorder the terms

4752 L^{2} - 1 = 0

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

4752 L^{2} = 0 + 1

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

4752 L^{2} = 1

Divide both sides

\frac{4752 L ^{2}}{4752} = \frac{1}{4752}

Divide the numbers

L^{2} = \frac{1}{4752}

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

L = \pm \frac{1}{4752}

Simplify the expression

More Steps

Evaluate

\frac{1}{4752}

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

\frac{1}{4752}

Simplify the radical expression

\frac{1}{4752}

Simplify the radical expression

More Steps

Evaluate

4752

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

144 \times 33

Write the number in exponential form with the base of 12

1 2^{2} \times 33

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

1 2^{2} \times 33

Reduce the index of the radical and exponent with 2

1233

\frac{1}{12 33}

Multiply by the Conjugate

\frac{33}{12 33 \times 33}

Multiply the numbers

More Steps

Evaluate

1233 \times 33

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

12 \times 33

Multiply the terms

396

\frac{33}{396}

L = \pm \frac{33}{396}

Separate the equation into 2 possible cases

L = \frac{33}{396} L = - \frac{33}{396}

Solution

L_{1} = - \frac{33}{396}, L_{2} = \frac{33}{396}

Alternative Form

L_{1} \approx - 0.014506, L_{2} \approx 0.014506

Show Solution