Solve h^654-23402

Question

Simplify the expression

54 h^{6} - 23402

Evaluate

h^{6} \times 54 - 23402

Solution

54 h^{6} - 23402

Show Solution

2 (27 h^{6} - 11701)

Evaluate

h^{6} \times 54 - 23402

Use the commutative property to reorder the terms

54 h^{6} - 23402

Solution

2 (27 h^{6} - 11701)

Show Solution

h_{1} = - \frac{6 315927}{3}, h_{2} = \frac{6 315927}{3}

Alternative Form

h_{1} \approx - 2.750911, h_{2} \approx 2.750911

Evaluate

h^{6} \times 54 - 23402

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

h^{6} \times 54 - 23402 = 0

Use the commutative property to reorder the terms

54 h^{6} - 23402 = 0

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

54 h^{6} = 0 + 23402

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

54 h^{6} = 23402

Divide both sides

\frac{54 h ^{6}}{54} = \frac{23402}{54}

Divide the numbers

h^{6} = \frac{23402}{54}

Cancel out the common factor 2

h^{6} = \frac{11701}{27}

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

h = \pm 6 \frac{11701}{27}

Simplify the expression

More Steps

Evaluate

6 \frac{11701}{27}

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

\frac{6 11701}{6 27}

Simplify the radical expression

More Steps

Evaluate

627

Write the number in exponential form with the base of 3

6 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{6 11701}{3}

Multiply by the Conjugate

\frac{6 11701 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

611701 \times 3

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

611701 \times 6 3^{3}

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

6 11701 \times 3^{3}

Calculate the product

6315927

\frac{6 315927}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6 315927}{3}

h = \pm \frac{6 315927}{3}

Separate the equation into 2 possible cases

h = \frac{6 315927}{3} h = - \frac{6 315927}{3}

Solution

h_{1} = - \frac{6 315927}{3}, h_{2} = \frac{6 315927}{3}

Alternative Form

h_{1} \approx - 2.750911, h_{2} \approx 2.750911

Show Solution