Solve r^4216-1 - ScanMath

Question

Simplify the expression

216 r^{4} - 1

Evaluate

r^{4} \times 216 - 1

Solution

216 r^{4} - 1

Show Solution

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

Alternative Form

r_{1} \approx - 0.260847, r_{2} \approx 0.260847

Evaluate

r^{4} \times 216 - 1

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

r^{4} \times 216 - 1 = 0

Use the commutative property to reorder the terms

216 r^{4} - 1 = 0

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

216 r^{4} = 0 + 1

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

216 r^{4} = 1

Divide both sides

\frac{216 r ^{4}}{216} = \frac{1}{216}

Divide the numbers

r^{4} = \frac{1}{216}

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

r = \pm 4 \frac{1}{216}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{216}

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

\frac{4 1}{4 216}

Simplify the radical expression

\frac{1}{4 216}

Multiply by the Conjugate

\frac{4 21 6 ^{3}}{4 216 \times 4 21 6 ^{3}}

Simplify

\frac{6 ^{2} 4 6}{4 216 \times 4 21 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

4216 \times 4 21 6^{3}

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

4 216 \times 21 6^{3}

Calculate the product

4 21 6^{4}

Transform the expression

4 6^{12}

Reduce the index of the radical and exponent with 4

6^{3}

\frac{6 ^{2} 4 6}{6 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{6 ^{2}}{6 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{6 ^{3 - 2}}

Subtract the terms

\frac{1}{6 ^{1}}

Simplify

\frac{1}{6}

\frac{4 6}{6}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

r_{1} \approx - 0.260847, r_{2} \approx 0.260847

Show Solution