Solve r^622-16 - ScanMath

Question

Simplify the expression

22 r^{6} - 16

Evaluate

r^{6} \times 22 - 16

Solution

22 r^{6} - 16

Show Solution

2 (11 r^{6} - 8)

Evaluate

r^{6} \times 22 - 16

Use the commutative property to reorder the terms

22 r^{6} - 16

Solution

2 (11 r^{6} - 8)

Show Solution

r_{1} = - \frac{6 8 \times 1 1 ^{5}}{11}, r_{2} = \frac{6 8 \times 1 1 ^{5}}{11}

Alternative Form

r_{1} \approx - 0.948308, r_{2} \approx 0.948308

Evaluate

r^{6} \times 22 - 16

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

r^{6} \times 22 - 16 = 0

Use the commutative property to reorder the terms

22 r^{6} - 16 = 0

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

22 r^{6} = 0 + 16

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

22 r^{6} = 16

Divide both sides

\frac{22 r ^{6}}{22} = \frac{16}{22}

Divide the numbers

r^{6} = \frac{16}{22}

Cancel out the common factor 2

r^{6} = \frac{8}{11}

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

r = \pm 6 \frac{8}{11}

Simplify the expression

More Steps

Evaluate

6 \frac{8}{11}

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

\frac{6 8}{6 11}

Simplify the radical expression

More Steps

Evaluate

68

Write the number in exponential form with the base of 2

6 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{6 11}

Multiply by the Conjugate

\frac{2 \times 6 1 1 ^{5}}{6 11 \times 6 1 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

2 \times 6 1 1^{5}

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

6 2^{3} \times 6 1 1^{5}

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

6 2^{3} \times 1 1^{5}

Calculate the product

6 8 \times 1 1^{5}

\frac{6 8 \times 1 1 ^{5}}{6 11 \times 6 1 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

611 \times 6 1 1^{5}

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

6 11 \times 1 1^{5}

Calculate the product

6 1 1^{6}

Reduce the index of the radical and exponent with 6

11

\frac{6 8 \times 1 1 ^{5}}{11}

r = \pm \frac{6 8 \times 1 1 ^{5}}{11}

Separate the equation into 2 possible cases

r = \frac{6 8 \times 1 1 ^{5}}{11} r = - \frac{6 8 \times 1 1 ^{5}}{11}

Solution

r_{1} = - \frac{6 8 \times 1 1 ^{5}}{11}, r_{2} = \frac{6 8 \times 1 1 ^{5}}{11}

Alternative Form

r_{1} \approx - 0.948308, r_{2} \approx 0.948308

Show Solution