Solve (27-18r^2r^2)

Question

Simplify the expression

27 - 18 r^{4}

Evaluate

27 - 18 r^{2} \times r^{2}

Solution

More Steps

Evaluate

18 r^{2} \times r^{2}

Multiply the terms with the same base by adding their exponents

18 r^{2 + 2}

Add the numbers

18 r^{4}

27 - 18 r^{4}

Show Solution

Factor the expression

9 (3 - 2 r^{4})

Evaluate

27 - 18 r^{2} \times r^{2}

Multiply

More Steps

Evaluate

18 r^{2} \times r^{2}

Multiply the terms with the same base by adding their exponents

18 r^{2 + 2}

Add the numbers

18 r^{4}

27 - 18 r^{4}

Solution

9 (3 - 2 r^{4})

Show Solution

Find the roots

r_{1} = - \frac{4 24}{2}, r_{2} = \frac{4 24}{2}

Alternative Form

r_{1} \approx - 1.106682, r_{2} \approx 1.106682

Evaluate

(27 - 18 r^{2} \times r^{2})

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

27 - 18 r^{2} \times r^{2} = 0

Multiply

More Steps

Multiply the terms

18 r^{2} \times r^{2}

Multiply the terms with the same base by adding their exponents

18 r^{2 + 2}

Add the numbers

18 r^{4}

27 - 18 r^{4} = 0

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

- 18 r^{4} = 0 - 27

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

- 18 r^{4} = - 27

Change the signs on both sides of the equation

18 r^{4} = 27

Divide both sides

\frac{18 r ^{4}}{18} = \frac{27}{18}

Divide the numbers

r^{4} = \frac{27}{18}

Cancel out the common factor 9

r^{4} = \frac{3}{2}

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

r = \pm 4 \frac{3}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{2}

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

\frac{4 3}{4 2}

Multiply by the Conjugate

\frac{4 3 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 3 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 48

The product of roots with the same index is equal to the root of the product

4 3 \times 8

Calculate the product

424

\frac{4 24}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

The product of roots with the same index is equal to the root of the product

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 24}{2}

r = \pm \frac{4 24}{2}

Separate the equation into 2 possible cases

r = \frac{4 24}{2} r = - \frac{4 24}{2}

Solution

r_{1} = - \frac{4 24}{2}, r_{2} = \frac{4 24}{2}

Alternative Form

r_{1} \approx - 1.106682, r_{2} \approx 1.106682

Show Solution