Solve r^4224-16 - ScanMath

Question

Simplify the expression

224 r^{4} - 16

Evaluate

r^{4} \times 224 - 16

Solution

224 r^{4} - 16

Show Solution

16 (14 r^{4} - 1)

Evaluate

r^{4} \times 224 - 16

Use the commutative property to reorder the terms

224 r^{4} - 16

Solution

16 (14 r^{4} - 1)

Show Solution

r_{1} = - \frac{4 2744}{14}, r_{2} = \frac{4 2744}{14}

Alternative Form

r_{1} \approx - 0.516973, r_{2} \approx 0.516973

Evaluate

r^{4} \times 224 - 16

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

r^{4} \times 224 - 16 = 0

Use the commutative property to reorder the terms

224 r^{4} - 16 = 0

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

224 r^{4} = 0 + 16

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

224 r^{4} = 16

Divide both sides

\frac{224 r ^{4}}{224} = \frac{16}{224}

Divide the numbers

r^{4} = \frac{16}{224}

Cancel out the common factor 16

r^{4} = \frac{1}{14}

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

r = \pm 4 \frac{1}{14}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{14}

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

\frac{4 1}{4 14}

Simplify the radical expression

\frac{1}{4 14}

Multiply by the Conjugate

\frac{4 1 4 ^{3}}{4 14 \times 4 1 4 ^{3}}

Simplify

\frac{4 2744}{4 14 \times 4 1 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

414 \times 4 1 4^{3}

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

4 14 \times 1 4^{3}

Calculate the product

4 1 4^{4}

Reduce the index of the radical and exponent with 4

14

\frac{4 2744}{14}

r = \pm \frac{4 2744}{14}

Separate the equation into 2 possible cases

r = \frac{4 2744}{14} r = - \frac{4 2744}{14}

Solution

r_{1} = - \frac{4 2744}{14}, r_{2} = \frac{4 2744}{14}

Alternative Form

r_{1} \approx - 0.516973, r_{2} \approx 0.516973

Show Solution