Solve 22J^611-4 - Socratic AI (ScanMath)

问题

Simplify the expression

242 J^{6} - 4

Evaluate

22 J^{6} \times 11 - 4

解题方案

242 J^{6} - 4

显示解题方案

2 (121 J^{6} - 2)

Evaluate

22 J^{6} \times 11 - 4

Multiply the terms

242 J^{6} - 4

解题方案

2 (121 J^{6} - 2)

显示解题方案

J_{1} = - \frac{6 29282}{11}, J_{2} = \frac{6 29282}{11}

Alternative Form

J_{1} \approx - 0.504709, J_{2} \approx 0.504709

Evaluate

22 J^{6} \times 11 - 4

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

22 J^{6} \times 11 - 4 = 0

Multiply the terms

242 J^{6} - 4 = 0

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

242 J^{6} = 0 + 4

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

242 J^{6} = 4

Divide both sides

\frac{242 J ^{6}}{242} = \frac{4}{242}

Divide the numbers

J^{6} = \frac{4}{242}

Cancel out the common factor 2

J^{6} = \frac{2}{121}

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

J = \pm 6 \frac{2}{121}

Simplify the expression

更多步骤

Evaluate

6 \frac{2}{121}

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

\frac{6 2}{6 121}

Simplify the radical expression

更多步骤

Evaluate

6121

Write the number in exponential form with the base of 11

6 1 1^{2}

Reduce the index of the radical and exponent with 2

311

\frac{6 2}{3 11}

Multiply by the Conjugate

\frac{6 2 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{6 2 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

更多步骤

Evaluate

62 \times 3121

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

62 \times 6 12 1^{2}

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

6 2 \times 12 1^{2}

Calculate the product

629282

\frac{6 29282}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

更多步骤

Evaluate

311 \times 3 1 1^{2}

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

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{6 29282}{11}

J = \pm \frac{6 29282}{11}

Separate the equation into 2 possible cases

J = \frac{6 29282}{11} J = - \frac{6 29282}{11}

解题方案

J_{1} = - \frac{6 29282}{11}, J_{2} = \frac{6 29282}{11}

Alternative Form

J_{1} \approx - 0.504709, J_{2} \approx 0.504709

显示解题方案