Taming the Surd: Simplifying √50
Break down the number under the root to find perfect squares and simplify.
Equation
y = 2^2 * x
Graph
Table
| x | y |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
| 6 | 24 |
| 7 | 28 |
| 8 | 32 |
| 9 | 36 |
| 10 | 40 |
What this lesson covers
What you do
You shape the function y = a^2 * x and watch the graph answer.
Challenges to clear
- (a√2)² = a²·2: slide a so the x = 2 row shows 50 — then √50 = 5√2.
- Same a: the x = 3 row shows 75, so √75 = 5√3 too.
- Tame √98 the same way. Slide a to the whole number whose square is the biggest factor of 98.
- Now slide b to whatever is left under the root, until the x = 1 row reads 98 — so √98 = 7√2.
Check yourself
Why is √50 equal to 5√2?
- Because 50 = 25 × 2, and √(25 × 2) = √25 × √2 = 5√2. — correct
- Because 50 is an even number, so we divide by 2.
- Because 5 × 2 = 10, and 10² = 100, which is close to 50.
- Because √50 is approximately 7, and 5 + 2 = 7.
Think about it
- √50 = √(25 × 2) = 5√2. In y = a²·x, which a makes the x = 2 row show 50?