Solve 12n^24-3 - ScanMath

Question

Simplify the expression

48 n^{2} - 3

Evaluate

12 n^{2} \times 4 - 3

Solution

48 n^{2} - 3

Show Solution

3 (4 n - 1) (4 n + 1)

Evaluate

12 n^{2} \times 4 - 3

Evaluate

48 n^{2} - 3

Factor out 3 from the expression

3 (16 n^{2} - 1)

Solution

More Steps

Evaluate

16 n^{2} - 1

Rewrite the expression in exponential form

(4 n)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(4 n - 1) (4 n + 1)

3 (4 n - 1) (4 n + 1)

Show Solution

n_{1} = - \frac{1}{4}, n_{2} = \frac{1}{4}

Alternative Form

n_{1} = - 0.25, n_{2} = 0.25

Evaluate

12 n^{2} \times 4 - 3

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

12 n^{2} \times 4 - 3 = 0

Multiply the terms

48 n^{2} - 3 = 0

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

48 n^{2} = 0 + 3

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

48 n^{2} = 3

Divide both sides

\frac{48 n ^{2}}{48} = \frac{3}{48}

Divide the numbers

n^{2} = \frac{3}{48}

Cancel out the common factor 3

n^{2} = \frac{1}{16}

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

n = \pm \frac{1}{16}

Simplify the expression

More Steps

Evaluate

\frac{1}{16}

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

\frac{1}{16}

Simplify the radical expression

\frac{1}{16}

Simplify the radical expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{1}{4}

n = \pm \frac{1}{4}

Separate the equation into 2 possible cases

n = \frac{1}{4} n = - \frac{1}{4}

Solution

n_{1} = - \frac{1}{4}, n_{2} = \frac{1}{4}

Alternative Form

n_{1} = - 0.25, n_{2} = 0.25

Show Solution