Solve r^4228-16 - ScanMath

Question

Simplify the expression

228 r^{4} - 16

Evaluate

r^{4} \times 228 - 16

Solution

228 r^{4} - 16

Show Solution

4 (57 r^{4} - 4)

Evaluate

r^{4} \times 228 - 16

Use the commutative property to reorder the terms

228 r^{4} - 16

Solution

4 (57 r^{4} - 4)

Show Solution

r_{1} = - \frac{4 4 \times 5 7 ^{3}}{57}, r_{2} = \frac{4 4 \times 5 7 ^{3}}{57}

Alternative Form

r_{1} \approx - 0.514691, r_{2} \approx 0.514691

Evaluate

r^{4} \times 228 - 16

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

r^{4} \times 228 - 16 = 0

Use the commutative property to reorder the terms

228 r^{4} - 16 = 0

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

228 r^{4} = 0 + 16

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

228 r^{4} = 16

Divide both sides

\frac{228 r ^{4}}{228} = \frac{16}{228}

Divide the numbers

r^{4} = \frac{16}{228}

Cancel out the common factor 4

r^{4} = \frac{4}{57}

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

r = \pm 4 \frac{4}{57}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{57}

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

\frac{4 4}{4 57}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{4 57}

Multiply by the Conjugate

\frac{2 \times 4 5 7 ^{3}}{4 57 \times 4 5 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

2 \times 4 5 7^{3}

Use n a = mn a^{m} to expand the expression

4 2^{2} \times 4 5 7^{3}

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

4 2^{2} \times 5 7^{3}

Calculate the product

4 4 \times 5 7^{3}

\frac{4 4 \times 5 7 ^{3}}{4 57 \times 4 5 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

457 \times 4 5 7^{3}

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

4 57 \times 5 7^{3}

Calculate the product

4 5 7^{4}

Reduce the index of the radical and exponent with 4

57

\frac{4 4 \times 5 7 ^{3}}{57}

r = \pm \frac{4 4 \times 5 7 ^{3}}{57}

Separate the equation into 2 possible cases

r = \frac{4 4 \times 5 7 ^{3}}{57} r = - \frac{4 4 \times 5 7 ^{3}}{57}

Solution

r_{1} = - \frac{4 4 \times 5 7 ^{3}}{57}, r_{2} = \frac{4 4 \times 5 7 ^{3}}{57}

Alternative Form

r_{1} \approx - 0.514691, r_{2} \approx 0.514691

Show Solution