Solve r^4216-9 - ScanMath

Question

Simplify the expression

216 r^{4} - 9

Evaluate

r^{4} \times 216 - 9

Solution

216 r^{4} - 9

Show Solution

9 (24 r^{4} - 1)

Evaluate

r^{4} \times 216 - 9

Use the commutative property to reorder the terms

216 r^{4} - 9

Solution

9 (24 r^{4} - 1)

Show Solution

r_{1} = - \frac{4 54}{6}, r_{2} = \frac{4 54}{6}

Alternative Form

r_{1} \approx - 0.451801, r_{2} \approx 0.451801

Evaluate

r^{4} \times 216 - 9

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

r^{4} \times 216 - 9 = 0

Use the commutative property to reorder the terms

216 r^{4} - 9 = 0

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

216 r^{4} = 0 + 9

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

216 r^{4} = 9

Divide both sides

\frac{216 r ^{4}}{216} = \frac{9}{216}

Divide the numbers

r^{4} = \frac{9}{216}

Cancel out the common factor 9

r^{4} = \frac{1}{24}

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

r = \pm 4 \frac{1}{24}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{24}

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

\frac{4 1}{4 24}

Simplify the radical expression

\frac{1}{4 24}

Multiply by the Conjugate

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

Simplify

\frac{4 4 54}{4 24 \times 4 2 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

424 \times 4 2 4^{3}

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

4 24 \times 2 4^{3}

Calculate the product

4 2 4^{4}

Reduce the index of the radical and exponent with 4

24

\frac{4 4 54}{24}

Cancel out the common factor 4

\frac{4 54}{6}

r = \pm \frac{4 54}{6}

Separate the equation into 2 possible cases

r = \frac{4 54}{6} r = - \frac{4 54}{6}

Solution

r_{1} = - \frac{4 54}{6}, r_{2} = \frac{4 54}{6}

Alternative Form

r_{1} \approx - 0.451801, r_{2} \approx 0.451801

Show Solution