Graphing Calculator Radical (20-1)

Question 1

How do you enter a square root or higher root on a TI-84/T184 graphing calculator?

Answer 1

For square root, press √ (or 2nd → x² for some calculators). For nth roots, press MATH → 4:root( → enter n, then the number.

Example: cube root of 27 → MATH → 4:root( → 3, 27 → ENTER → 3.

Question 2

How do you simplify radical expressions using a graphing calculator?

Answer 2

Enter the number under the radical. The calculator will give a decimal, but to check exact simplification, divide the original number by squares of factors to find the largest perfect square. Use decimal to verify: 5√2 ≈ 7.071, √50 ≈ 7.071.

Example: √50.

Question 3

How do you perform addition or subtraction of radicals on a graphing calculator?

Answer 3

You must enter each radical separately. The calculator gives a decimal: 4.242 + 2.828 = 7.070. You can then relate back to exact simplified form: 3√2 + 2√2 = 5√2.

Example: √18 + √8 → (√18) + (√8).

Question 4

How do you multiply radicals using a graphing calculator?

Answer 4

Enter as normal multiplication.

Example: √3 * √12 → √3 * √12 = √36 → calculator gives 6.

Question 5

How do you divide radicals on a graphing calculator?

Answer 5

Enter as normal division. Check simplified form: √50/√2 = √25 = 5.

Example: √50 ÷ √2 → 7.071 ÷ 1.414 ≈ 5.

Question 6

How do you solve radical equations using a graphing calculator?

Answer 6

Enter two functions: Y1 = √(X+3), Y2 = 5. GRAPH → 2nd → TRACE → intersect.

Example: √(x+3) = 5.

Question 7

How do you check for extraneous solutions in radical equations on a graphing calculator?

Answer 7

Plug your solution(s) back into the original equation using 2nd → TRACE → value. If the left-hand side ≠ right-hand side, it’s extraneous.

Question 8

How do you graph radical functions?

Answer 8

Enter function in Y= (e.g., Y1 = √(X+2) - 1). Adjust WINDOW to see key points, intercepts, and domain. Use TRACE or TABLE to find values.

Question 9

How can you transform radical graphs on a graphing calculator?

Answer 9

• Vertical shifts: Y1 = √(X) + 3 → shift up 3 units
• Horizontal shifts: Y1 = √(X-4) → shift right 4 units
• Reflections: Y1 = -√(X) → reflect over X-axis
• Vertical stretches: Y1 = 2√(X) → stretch by factor 2.

Question 10

Practice card: Graph Y = √(X-3) + 2 and find Y-intercept.

Answer 10

Y-intercept: set X=0 → √(-3) + 2 → undefined. Graph confirms no Y-intercept.

Question 11

Practice card: Solve √(X+5) = 7 using graphing calculator.

Answer 11

Enter Y1 = √(X+5), Y2 = 7 → GRAPH → 2nd → TRACE → intersect → X=44.

Question 12

Practice card: Simplify √(72) and check with graphing calculator.

Answer 12

Calculator decimal: √72 ≈ 8.485. Simplify: √72 = √36*2 = 6√2 → 6√2 ≈ 8.485. Verified.