Solve r^4412-9 - ScanMath

Question

Simplify the expression

412 r^{4} - 9

Evaluate

r^{4} \times 412 - 9

Solution

412 r^{4} - 9

Show Solution

r_{1} = - \frac{4 9 \times 41 2 ^{3}}{412}, r_{2} = \frac{4 9 \times 41 2 ^{3}}{412}

Alternative Form

r_{1} \approx - 0.384447, r_{2} \approx 0.384447

Evaluate

r^{4} \times 412 - 9

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

r^{4} \times 412 - 9 = 0

Use the commutative property to reorder the terms

412 r^{4} - 9 = 0

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

412 r^{4} = 0 + 9

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

412 r^{4} = 9

Divide both sides

\frac{412 r ^{4}}{412} = \frac{9}{412}

Divide the numbers

r^{4} = \frac{9}{412}

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

r = \pm 4 \frac{9}{412}

Simplify the expression

More Steps

Evaluate

4 \frac{9}{412}

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

\frac{4 9}{4 412}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{4 412}

Multiply by the Conjugate

\frac{3 \times 4 41 2 ^{3}}{4 412 \times 4 41 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

3 \times 4 41 2^{3}

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

4 3^{2} \times 4 41 2^{3}

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

4 3^{2} \times 41 2^{3}

Calculate the product

4 9 \times 41 2^{3}

\frac{4 9 \times 41 2 ^{3}}{4 412 \times 4 41 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

4412 \times 4 41 2^{3}

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

4 412 \times 41 2^{3}

Calculate the product

4 41 2^{4}

Reduce the index of the radical and exponent with 4

412

\frac{4 9 \times 41 2 ^{3}}{412}

r = \pm \frac{4 9 \times 41 2 ^{3}}{412}

Separate the equation into 2 possible cases

r = \frac{4 9 \times 41 2 ^{3}}{412} r = - \frac{4 9 \times 41 2 ^{3}}{412}

Solution

r_{1} = - \frac{4 9 \times 41 2 ^{3}}{412}, r_{2} = \frac{4 9 \times 41 2 ^{3}}{412}

Alternative Form

r_{1} \approx - 0.384447, r_{2} \approx 0.384447

Show Solution