Solve r^4222-4 - ScanMath

Question

Simplify the expression

222 r^{4} - 4

Evaluate

r^{4} \times 222 - 4

Solution

222 r^{4} - 4

Show Solution

2 (111 r^{4} - 2)

Evaluate

r^{4} \times 222 - 4

Use the commutative property to reorder the terms

222 r^{4} - 4

Solution

2 (111 r^{4} - 2)

Show Solution

r_{1} = - \frac{4 2 \times 11 1 ^{3}}{111}, r_{2} = \frac{4 2 \times 11 1 ^{3}}{111}

Alternative Form

r_{1} \approx - 0.366376, r_{2} \approx 0.366376

Evaluate

r^{4} \times 222 - 4

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

r^{4} \times 222 - 4 = 0

Use the commutative property to reorder the terms

222 r^{4} - 4 = 0

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

222 r^{4} = 0 + 4

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

222 r^{4} = 4

Divide both sides

\frac{222 r ^{4}}{222} = \frac{4}{222}

Divide the numbers

r^{4} = \frac{4}{222}

Cancel out the common factor 2

r^{4} = \frac{2}{111}

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

r = \pm 4 \frac{2}{111}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{111}

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

\frac{4 2}{4 111}

Multiply by the Conjugate

\frac{4 2 \times 4 11 1 ^{3}}{4 111 \times 4 11 1 ^{3}}

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

\frac{4 2 \times 11 1 ^{3}}{4 111 \times 4 11 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

4111 \times 4 11 1^{3}

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

4 111 \times 11 1^{3}

Calculate the product

4 11 1^{4}

Reduce the index of the radical and exponent with 4

111

\frac{4 2 \times 11 1 ^{3}}{111}

r = \pm \frac{4 2 \times 11 1 ^{3}}{111}

Separate the equation into 2 possible cases

r = \frac{4 2 \times 11 1 ^{3}}{111} r = - \frac{4 2 \times 11 1 ^{3}}{111}

Solution

r_{1} = - \frac{4 2 \times 11 1 ^{3}}{111}, r_{2} = \frac{4 2 \times 11 1 ^{3}}{111}

Alternative Form

r_{1} \approx - 0.366376, r_{2} \approx 0.366376

Show Solution