Square Root by Prime Factors
Factorise 144 into primes, pair them up, and pull one from each pair.
Equation
y = 2 * sqrt(x)
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | 2 |
| 2 | 2.83 |
| 3 | 3.46 |
| 4 | 4 |
| 5 | 4.47 |
| 6 | 4.9 |
| 7 | 5.29 |
| 8 | 5.66 |
| 9 | 6 |
What this lesson covers
What you do
You shape the function y = a * sqrt(x) and watch the graph answer.
Challenges to clear
- 144 = (2·2·3)²: pull ONE from each pair to get 12. Slide a to 12 and check x = 1 gives 12.
- Scaling check: at x = 4, y = 12 · √4 = 24.
- There is a square hiding under the root. Slide b to 4 so it can come out as a 2.
- Now the outside multiplier: x = 1 must read 30. With the 2 already out, a is 15.
Check yourself
Why do we pair up prime factors when finding a square root?
If x = sqrt(2 * 2 * 5 * 5 * 7), what is the value of x?
- Because sqrt(a * a) = a. A pair of identical numbers under the root cancels out to a single number. — correct
- Because we need an even number of factors to make the number look symmetrical.
- Because prime factors must always come in groups of two.
- Because adding the pairs gives the correct answer.
- 2 * 5 * sqrt(7) — correct
- 2 * 5 * 7 = 70
- 2 * 5 * 7 * 7 = 490
- sqrt(2) * sqrt(5) * sqrt(7)