Solve h^5216-361 - ScanMath

Question

Simplify the expression

216 h^{5} - 361

Evaluate

h^{5} \times 216 - 361

Solution

216 h^{5} - 361

Show Solution

h = \frac{5 12996}{6}

Alternative Form

h \approx 1.108181

Evaluate

h^{5} \times 216 - 361

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

h^{5} \times 216 - 361 = 0

Use the commutative property to reorder the terms

216 h^{5} - 361 = 0

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

216 h^{5} = 0 + 361

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

216 h^{5} = 361

Divide both sides

\frac{216 h ^{5}}{216} = \frac{361}{216}

Divide the numbers

h^{5} = \frac{361}{216}

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

5 h^{5} = 5 \frac{361}{216}

Calculate

h = 5 \frac{361}{216}

Solution

More Steps

Evaluate

5 \frac{361}{216}

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

\frac{5 361}{5 216}

Multiply by the Conjugate

\frac{5 361 \times 5 21 6 ^{4}}{5 216 \times 5 21 6 ^{4}}

Simplify

\frac{5 361 \times 6 ^{2} 5 36}{5 216 \times 5 21 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

5361 \times 6^{2} 536

Multiply the terms

512996 \times 6^{2}

Use the commutative property to reorder the terms

6^{2} 512996

\frac{6 ^{2} 5 12996}{5 216 \times 5 21 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

5216 \times 5 21 6^{4}

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

5 216 \times 21 6^{4}

Calculate the product

5 21 6^{5}

Transform the expression

5 6^{15}

Reduce the index of the radical and exponent with 5

6^{3}

\frac{6 ^{2} 5 12996}{6 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{6 ^{2}}{6 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{6 ^{3 - 2}}

Subtract the terms

\frac{1}{6 ^{1}}

Simplify

\frac{1}{6}

\frac{5 12996}{6}

h = \frac{5 12996}{6}

Alternative Form

h \approx 1.108181

Show Solution