Solve h^5216-3002025

Question

Simplify the expression

216 h^{5} - 3002025

Evaluate

h^{5} \times 216 - 3002025

Solution

216 h^{5} - 3002025

Show Solution

3 (72 h^{5} - 1000675)

Evaluate

h^{5} \times 216 - 3002025

Use the commutative property to reorder the terms

216 h^{5} - 3002025

Solution

3 (72 h^{5} - 1000675)

Show Solution

h = \frac{5 1000675 \times 7 2 ^{4}}{72}

Alternative Form

h \approx 6.738948

Evaluate

h^{5} \times 216 - 3002025

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

h^{5} \times 216 - 3002025 = 0

Use the commutative property to reorder the terms

216 h^{5} - 3002025 = 0

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

216 h^{5} = 0 + 3002025

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

216 h^{5} = 3002025

Divide both sides

\frac{216 h ^{5}}{216} = \frac{3002025}{216}

Divide the numbers

h^{5} = \frac{3002025}{216}

Cancel out the common factor 3

h^{5} = \frac{1000675}{72}

Take the 5 -th root on both sides of the equation

5 h^{5} = 5 \frac{1000675}{72}

Calculate

h = 5 \frac{1000675}{72}

Solution

More Steps

Evaluate

5 \frac{1000675}{72}

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

\frac{5 1000675}{5 72}

Multiply by the Conjugate

\frac{5 1000675 \times 5 7 2 ^{4}}{5 72 \times 5 7 2 ^{4}}

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

\frac{5 1000675 \times 7 2 ^{4}}{5 72 \times 5 7 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

572 \times 5 7 2^{4}

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

5 72 \times 7 2^{4}

Calculate the product

5 7 2^{5}

Reduce the index of the radical and exponent with 5

72

\frac{5 1000675 \times 7 2 ^{4}}{72}

h = \frac{5 1000675 \times 7 2 ^{4}}{72}

Alternative Form

h \approx 6.738948

Show Solution