Solve for y*y*. Express your answer as an integer or integers or in simplest radical form.

10, y, cubed, plus, 6, equals, 146

10*y*3+6=

146

We are given the equation:

\[
10y^3 + 6 = 146
\]

### Step 1: Subtract 6 from both sides to isolate the cubic term.
\[
10y^3 = 146 - 6
\]
\[
10y^3 = 140
\]

### Step 2: Divide both sides by 10.
\[
y^3 = \frac{140}{10}
\]
\[
y^3 = 14
\]

### Step 3: Solve for \(y\) by taking the cube root of both sides.
\[
y = \sqrt[3]{14}
\]

Since \(14\) is not a perfect cube, the simplest form of \(y\) is:
\[
y = \sqrt[3]{14}
\]

This is the simplest radical form of \(y\).

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Would you like more details or have any questions?

Here are 5 related questions:
1. What happens if the exponent is higher than 3?
2. How do you simplify a cube root expression?
3. Can cube roots of negative numbers be real?
4. How do you solve equations with both cube and square roots?
5. How do you approximate cube roots without a calculator?

**Tip:** Cube roots are not as common as square roots, but they play a key role when solving cubic equations like \(y^3 = 14\).

Solve for y. Express your answer as an integer or integers or in simplest radical form. 10 * y^3 + 6 = 146.

Explore how to solve the cubic equation 10y^3 + 6 = 146 using algebraic techniques. This step-by-step guide covers isolating the cubic term, dividing coefficients, and expressing the result in simplest radical form. Perfect for high school students learning advanced algebra.

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