Solve 45r^412-3033

Question

Simplify the expression

540 r^{4} - 3033

Evaluate

45 r^{4} \times 12 - 3033

Solution

540 r^{4} - 3033

Show Solution

9 (60 r^{4} - 337)

Evaluate

45 r^{4} \times 12 - 3033

Multiply the terms

540 r^{4} - 3033

Solution

9 (60 r^{4} - 337)

Show Solution

r_{1} = - \frac{4 337 \times 6 0 ^{3}}{60}, r_{2} = \frac{4 337 \times 6 0 ^{3}}{60}

Alternative Form

r_{1} \approx - 1.539464, r_{2} \approx 1.539464

Evaluate

45 r^{4} \times 12 - 3033

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

45 r^{4} \times 12 - 3033 = 0

Multiply the terms

540 r^{4} - 3033 = 0

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

540 r^{4} = 0 + 3033

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

540 r^{4} = 3033

Divide both sides

\frac{540 r ^{4}}{540} = \frac{3033}{540}

Divide the numbers

r^{4} = \frac{3033}{540}

Cancel out the common factor 9

r^{4} = \frac{337}{60}

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

r = \pm 4 \frac{337}{60}

Simplify the expression

More Steps

Evaluate

4 \frac{337}{60}

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

\frac{4 337}{4 60}

Multiply by the Conjugate

\frac{4 337 \times 4 6 0 ^{3}}{4 60 \times 4 6 0 ^{3}}

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

\frac{4 337 \times 6 0 ^{3}}{4 60 \times 4 6 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

460 \times 4 6 0^{3}

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

4 60 \times 6 0^{3}

Calculate the product

4 6 0^{4}

Reduce the index of the radical and exponent with 4

60

\frac{4 337 \times 6 0 ^{3}}{60}

r = \pm \frac{4 337 \times 6 0 ^{3}}{60}

Separate the equation into 2 possible cases

r = \frac{4 337 \times 6 0 ^{3}}{60} r = - \frac{4 337 \times 6 0 ^{3}}{60}

Solution

r_{1} = - \frac{4 337 \times 6 0 ^{3}}{60}, r_{2} = \frac{4 337 \times 6 0 ^{3}}{60}

Alternative Form

r_{1} \approx - 1.539464, r_{2} \approx 1.539464

Show Solution