Solve r^4222-9 - ScanMath

Question

Simplify the expression

222 r^{4} - 9

Evaluate

r^{4} \times 222 - 9

Solution

222 r^{4} - 9

Show Solution

3 (74 r^{4} - 3)

Evaluate

r^{4} \times 222 - 9

Use the commutative property to reorder the terms

222 r^{4} - 9

Solution

3 (74 r^{4} - 3)

Show Solution

r_{1} = - \frac{4 3 \times 7 4 ^{3}}{74}, r_{2} = \frac{4 3 \times 7 4 ^{3}}{74}

Alternative Form

r_{1} \approx - 0.448717, r_{2} \approx 0.448717

Evaluate

r^{4} \times 222 - 9

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

r^{4} \times 222 - 9 = 0

Use the commutative property to reorder the terms

222 r^{4} - 9 = 0

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

222 r^{4} = 0 + 9

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

222 r^{4} = 9

Divide both sides

\frac{222 r ^{4}}{222} = \frac{9}{222}

Divide the numbers

r^{4} = \frac{9}{222}

Cancel out the common factor 3

r^{4} = \frac{3}{74}

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

r = \pm 4 \frac{3}{74}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{74}

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

\frac{4 3}{4 74}

Multiply by the Conjugate

\frac{4 3 \times 4 7 4 ^{3}}{4 74 \times 4 7 4 ^{3}}

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

\frac{4 3 \times 7 4 ^{3}}{4 74 \times 4 7 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

474 \times 4 7 4^{3}

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

4 74 \times 7 4^{3}

Calculate the product

4 7 4^{4}

Reduce the index of the radical and exponent with 4

74

\frac{4 3 \times 7 4 ^{3}}{74}

r = \pm \frac{4 3 \times 7 4 ^{3}}{74}

Separate the equation into 2 possible cases

r = \frac{4 3 \times 7 4 ^{3}}{74} r = - \frac{4 3 \times 7 4 ^{3}}{74}

Solution

r_{1} = - \frac{4 3 \times 7 4 ^{3}}{74}, r_{2} = \frac{4 3 \times 7 4 ^{3}}{74}

Alternative Form

r_{1} \approx - 0.448717, r_{2} \approx 0.448717

Show Solution