**High School Number Sense Lesson 92: Square Roots (2 or More)**

This concept builds upon our understanding of square roots (

**SquareRoot**) and simplifying them (

**SquareRootSim**). Most common on high school tests, it appeared

**7 times**this year, with a median placement at

**question # 35**.

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When multiplying two square roots together, we can manipulate the numbers in various ways:

- Multiply the numbers and then take the square root of their product
- Take a factor from one of the numbers and combine it with the other
**Double/Half**, etc.

**Example 1: √60 x √15 = ___**

- Double/Half this to get √30 x √30
- The answer is
**30**

**Example 2: √5 x √45 = ___**

- Take a factor of 5 from the second number and multiply it by the first.
- √(5 x 5) x √(45 ÷ 5) = √25 x √9 = 5 x 3 =
**15**

**Example 3: √24 x √54 = ___**

- Take a factor of 6 from the second number and multiply it by the first.
- √(24 x 6) x √(54 ÷ 6) = √(12 x 12) x √9 = 12 x 3 =
**36**

**Example 4: √18 x √50 = ___**

- Take a factor of 2 from either number and multiply it by the other.
- √36 x √25 = 6 x 5 =
**30**

**Example 5: 8√2 x 4√18 = ___**

- Group the square roots and multiply everything together.
- 8 x 4 x √2 x √18 = 32 x √(2 x 18) = 32 x √36 = 32 x 6 =
**192**

**Example 6: √(18)(50) ÷ √25 = ___**

- Double/Half this to get √(36)(25) ÷ √25
- The √25's cancel, so we're left with √36
- The answer is
**6**

**Up Next for High School: AddMultRoots**