Solve h^5216-225 - ScanMath

Question

Simplify the expression

216 h^{5} - 225

Evaluate

h^{5} \times 216 - 225

Solution

216 h^{5} - 225

Show Solution

9 (24 h^{5} - 25)

Evaluate

h^{5} \times 216 - 225

Use the commutative property to reorder the terms

216 h^{5} - 225

Solution

9 (24 h^{5} - 25)

Show Solution

h = \frac{5 25 \times 2 4 ^{4}}{24}

Alternative Form

h \approx 1.008198

Evaluate

h^{5} \times 216 - 225

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

h^{5} \times 216 - 225 = 0

Use the commutative property to reorder the terms

216 h^{5} - 225 = 0

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

216 h^{5} = 0 + 225

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

216 h^{5} = 225

Divide both sides

\frac{216 h ^{5}}{216} = \frac{225}{216}

Divide the numbers

h^{5} = \frac{225}{216}

Cancel out the common factor 9

h^{5} = \frac{25}{24}

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

5 h^{5} = 5 \frac{25}{24}

Calculate

h = 5 \frac{25}{24}

Solution

More Steps

Evaluate

5 \frac{25}{24}

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

\frac{5 25}{5 24}

Multiply by the Conjugate

\frac{5 25 \times 5 2 4 ^{4}}{5 24 \times 5 2 4 ^{4}}

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

\frac{5 25 \times 2 4 ^{4}}{5 24 \times 5 2 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

524 \times 5 2 4^{4}

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

5 24 \times 2 4^{4}

Calculate the product

5 2 4^{5}

Reduce the index of the radical and exponent with 5

24

\frac{5 25 \times 2 4 ^{4}}{24}

h = \frac{5 25 \times 2 4 ^{4}}{24}

Alternative Form

h \approx 1.008198

Show Solution