Evaluating Algebraic Expressions with Cube Roots
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 7: Real Numbers and the Pythagorean Theorem) learn to evaluate algebraic expressions containing cube roots by substituting values and applying order of operations. They compute the cube root first, then perform remaining operations.
Key Concepts
Property To evaluate an algebraic expression involving a cube root for a given value of a variable, substitute the value for the variable and simplify the expression using the order of operations.
Examples Evaluate $5\sqrt[3]{x}$ when $x = 8$: $$5\sqrt[3]{8} = 5(2) = 10$$ Evaluate $\sqrt[3]{x + 19}$ when $x = 8$: $$\sqrt[3]{8 + 19} = \sqrt[3]{27} = 3$$ Evaluate $10 4\sqrt[3]{x}$ when $x = 64$: $$10 4\sqrt[3]{ 64} = 10 4( 4) = 10 + 16 = 26$$.
Explanation This skill combines substitution with evaluating cube roots. First, replace the variable in the expression with its given numerical value. Next, follow the order of operations to simplify the expression. Remember to calculate the value of the cube root before performing any multiplication, division, addition, or subtraction outside the radical.
Common Questions
How do you evaluate an algebraic expression with a cube root?
Substitute the variable value into the expression, then evaluate the cube root first (following order of operations), then perform any remaining multiplication, addition, or subtraction.
How do you evaluate 5 times cube_root(x) when x = 8?
Substitute x = 8: 5 times cube_root(8) = 5 times 2 = 10.
Can you take the cube root of a negative number?
Yes. The cube root of a negative number is negative. For example, cube_root(-64) = -4 because (-4)^3 = -64.
What chapter in Big Ideas Math Advanced 2 covers evaluating expressions with cube roots?
Chapter 7: Real Numbers and the Pythagorean Theorem in Big Ideas Math Advanced 2 (Grade 7) covers evaluating algebraic expressions with cube roots.
What is the order of operations when a cube root is present?
Evaluate the cube root before performing multiplication, division, addition, or subtraction outside the radical.