Solve z^210z-11 - ScanMath

Question

Simplify the expression

10 z^{3} - 11

Evaluate

z^{2} \times 10 z - 11

Solution

More Steps

Evaluate

z^{2} \times 10 z

Multiply the terms with the same base by adding their exponents

z^{2 + 1} \times 10

Add the numbers

z^{3} \times 10

Use the commutative property to reorder the terms

10 z^{3}

10 z^{3} - 11

Show Solution

z = \frac{3 1100}{10}

Alternative Form

z \approx 1.03228

Evaluate

z^{2} \times 10 z - 11

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

z^{2} \times 10 z - 11 = 0

Multiply

More Steps

Multiply the terms

z^{2} \times 10 z

Multiply the terms with the same base by adding their exponents

z^{2 + 1} \times 10

Add the numbers

z^{3} \times 10

Use the commutative property to reorder the terms

10 z^{3}

10 z^{3} - 11 = 0

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

10 z^{3} = 0 + 11

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

10 z^{3} = 11

Divide both sides

\frac{10 z ^{3}}{10} = \frac{11}{10}

Divide the numbers

z^{3} = \frac{11}{10}

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

3 z^{3} = 3 \frac{11}{10}

Calculate

z = 3 \frac{11}{10}

Solution

More Steps

Evaluate

3 \frac{11}{10}

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

\frac{3 11}{3 10}

Multiply by the Conjugate

\frac{3 11 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 11 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3100

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

3 11 \times 100

Calculate the product

31100

\frac{3 1100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{3 1100}{10}

z = \frac{3 1100}{10}

Alternative Form

z \approx 1.03228

Show Solution