Solve l^232-25 - ScanMath

Question

Simplify the expression

32 l^{2} - 25

Evaluate

l^{2} \times 32 - 25

Solution

32 l^{2} - 25

Show Solution

l_{1} = - \frac{5 2}{8}, l_{2} = \frac{5 2}{8}

Alternative Form

l_{1} \approx - 0.883883, l_{2} \approx 0.883883

Evaluate

l^{2} \times 32 - 25

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

l^{2} \times 32 - 25 = 0

Use the commutative property to reorder the terms

32 l^{2} - 25 = 0

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

32 l^{2} = 0 + 25

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

32 l^{2} = 25

Divide both sides

\frac{32 l ^{2}}{32} = \frac{25}{32}

Divide the numbers

l^{2} = \frac{25}{32}

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

l = \pm \frac{25}{32}

Simplify the expression

More Steps

Evaluate

\frac{25}{32}

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

\frac{25}{32}

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}{32}

Simplify the radical expression

More Steps

Evaluate

32

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

16 \times 2

Write the number in exponential form with the base of 4

4^{2} \times 2

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

4^{2} \times 2

Reduce the index of the radical and exponent with 2

42

\frac{5}{4 2}

Multiply by the Conjugate

\frac{5 2}{4 2 \times 2}

Multiply the numbers

More Steps

Evaluate

42 \times 2

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

4 \times 2

Multiply the terms

8

\frac{5 2}{8}

l = \pm \frac{5 2}{8}

Separate the equation into 2 possible cases

l = \frac{5 2}{8} l = - \frac{5 2}{8}

Solution

l_{1} = - \frac{5 2}{8}, l_{2} = \frac{5 2}{8}

Alternative Form

l_{1} \approx - 0.883883, l_{2} \approx 0.883883

Show Solution