Solve 18C^454-3 - ScanMath

Question

Simplify the expression

972 C^{4} - 3

Evaluate

18 C^{4} \times 54 - 3

Solution

972 C^{4} - 3

Show Solution

3 (18 C^{2} - 1) (18 C^{2} + 1)

Evaluate

18 C^{4} \times 54 - 3

Evaluate

972 C^{4} - 3

Factor out 3 from the expression

3 (324 C^{4} - 1)

Solution

More Steps

Evaluate

324 C^{4} - 1

Rewrite the expression in exponential form

(18 C^{2})^{2} - 1^{2}

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

(18 C^{2} - 1) (18 C^{2} + 1)

3 (18 C^{2} - 1) (18 C^{2} + 1)

Show Solution

C_{1} = - \frac{2}{6}, C_{2} = \frac{2}{6}

Alternative Form

C_{1} \approx - 0.235702, C_{2} \approx 0.235702

Evaluate

18 C^{4} \times 54 - 3

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

18 C^{4} \times 54 - 3 = 0

Multiply the terms

972 C^{4} - 3 = 0

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

972 C^{4} = 0 + 3

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

972 C^{4} = 3

Divide both sides

\frac{972 C ^{4}}{972} = \frac{3}{972}

Divide the numbers

C^{4} = \frac{3}{972}

Cancel out the common factor 3

C^{4} = \frac{1}{324}

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

C = \pm 4 \frac{1}{324}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{324}

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

\frac{4 1}{4 324}

Simplify the radical expression

\frac{1}{4 324}

Simplify the radical expression

More Steps

Evaluate

4324

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

4 81 \times 4

Write the number in exponential form with the base of 3

4 3^{4} \times 4

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

4 3^{4} \times 44

Reduce the index of the radical and exponent with 4

344

Simplify the root

32

\frac{1}{3 2}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

32 \times 2

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

3 \times 2

Multiply the terms

6

\frac{2}{6}

C = \pm \frac{2}{6}

Separate the equation into 2 possible cases

C = \frac{2}{6} C = - \frac{2}{6}

Solution

C_{1} = - \frac{2}{6}, C_{2} = \frac{2}{6}

Alternative Form

C_{1} \approx - 0.235702, C_{2} \approx 0.235702

Show Solution