Solve a^380-900 - ScanMath

Question

Simplify the expression

80 a^{3} - 900

Evaluate

a^{3} \times 80 - 900

Solution

80 a^{3} - 900

Show Solution

20 (4 a^{3} - 45)

Evaluate

a^{3} \times 80 - 900

Use the commutative property to reorder the terms

80 a^{3} - 900

Solution

20 (4 a^{3} - 45)

Show Solution

a = \frac{3 90}{2}

Alternative Form

a \approx 2.240702

Evaluate

a^{3} \times 80 - 900

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

a^{3} \times 80 - 900 = 0

Use the commutative property to reorder the terms

80 a^{3} - 900 = 0

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

80 a^{3} = 0 + 900

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

80 a^{3} = 900

Divide both sides

\frac{80 a ^{3}}{80} = \frac{900}{80}

Divide the numbers

a^{3} = \frac{900}{80}

Cancel out the common factor 20

a^{3} = \frac{45}{4}

Take the 3 -th root on both sides of the equation

3 a^{3} = 3 \frac{45}{4}

Calculate

a = 3 \frac{45}{4}

Solution

More Steps

Evaluate

3 \frac{45}{4}

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

\frac{3 45}{3 4}

Multiply by the Conjugate

\frac{3 45 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{3 45 \times 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 232

Multiply the terms

390 \times 2

Use the commutative property to reorder the terms

2390

\frac{2 3 90}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 90}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

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

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

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 90}{2}

a = \frac{3 90}{2}

Alternative Form

a \approx 2.240702

Show Solution