Solve a^330-343 - Socratic AI (ScanMath)

Question

Simplify the expression

30 a^{3} - 343

Evaluate

a^{3} \times 30 - 343

Solution

30 a^{3} - 343

Show Solution

a = \frac{7 3 900}{30}

Alternative Form

a \approx 2.252809

Evaluate

a^{3} \times 30 - 343

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

a^{3} \times 30 - 343 = 0

Use the commutative property to reorder the terms

30 a^{3} - 343 = 0

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

30 a^{3} = 0 + 343

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

30 a^{3} = 343

Divide both sides

\frac{30 a ^{3}}{30} = \frac{343}{30}

Divide the numbers

a^{3} = \frac{343}{30}

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

3 a^{3} = 3 \frac{343}{30}

Calculate

a = 3 \frac{343}{30}

Solution

More Steps

Evaluate

3 \frac{343}{30}

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

\frac{3 343}{3 30}

Simplify the radical expression

More Steps

Evaluate

3343

Write the number in exponential form with the base of 7

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{7}{3 30}

Multiply by the Conjugate

\frac{7 3 3 0 ^{2}}{3 30 \times 3 3 0 ^{2}}

Simplify

\frac{7 3 900}{3 30 \times 3 3 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

330 \times 3 3 0^{2}

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

3 30 \times 3 0^{2}

Calculate the product

3 3 0^{3}

Reduce the index of the radical and exponent with 3

30

\frac{7 3 900}{30}

a = \frac{7 3 900}{30}

Alternative Form

a \approx 2.252809

Show Solution