Multiply Surds: Root of Product
See why root 2 times root 3 becomes root 6.
Equation
y = sqrt(2) * sqrt(x) - sqrt(5*x)
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | -0.82 |
| 2 | -1.16 |
| 3 | -1.42 |
| 4 | -1.64 |
| 5 | -1.84 |
| 6 | -2.01 |
| 7 | -2.17 |
| 8 | -2.33 |
| 9 | -2.47 |
What this lesson covers
What you do
You shape the function y = sqrt(m) * sqrt(x) - sqrt(k*x) and watch the graph answer.
Challenges to clear
- √m · √x = √(m·x): with m = 2, slide k to match — the difference is 0 at x = 3 only when k = m.
- Check x = 2 as well: √2·√2 = √4 = 2. Root times root is root of the product.
- Now the product runs the other way: √(3m·x) has to match √(k·x). Start by sliding m to 5.
- With m = 5 the left side is √3·√5·√x. Slide k until the difference is 0 at x = 4 — root times root is the root of the product, so k = 15.
Check yourself
Which rule correctly explains why sqrt(5) * sqrt(7) = sqrt(35)?
- sqrt(a) * sqrt(b) = sqrt(a * b). Multiply the numbers under the root. — correct
- sqrt(a) * sqrt(b) = sqrt(a + b). Add the numbers under the root.
- sqrt(a) * sqrt(b) = a * b. Remove the roots completely.
- sqrt(a) * sqrt(b) = sqrt(a) + sqrt(b). Keep roots separate but add them.
Think about it
- √2 × √3 — is it √5 or √6?