Geometric Mean Practice worksheet from Quizizz featuring 10 questions, including calculations and a right triangle diagram.

Let’s solve each question one by one, carefully.

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Question 1: Find the geometric mean of 8 and 18.

Geometric mean of two numbers = √(a × b)

So, √(8 × 18) = √(144) = 12

✔ Answer: B. 12

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Question 2: Find the geometric mean of 20 and 25.

√(20 × 25) = √(500)

Simplify √500:
500 = 100 × 5 → √(100 × 5) = √100 × √5 = 10√5

✔ Answer: C. 10√5

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Question 3: 15 is the geometric mean of 25 and what other number?

Let the unknown number be x.

Then: √(25 × x) = 15

Square both sides:
25x = 225
→ x = 225 ÷ 25 = 9

✔ Answer: B. 9

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Question 4: Find the geometric mean of 3 and 7.

√(3 × 7) = √21

✔ Answer: B. √21

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Question 5: 8√2 is the geometric mean of 16 and what other number?

Let the unknown number be x.

Then: √(16 × x) = 8√2

Square both sides:
16x = (8√2)² = 64 × 2 = 128
→ x = 128 ÷ 16 = 8

Wait — let’s check:
If x = 8, then geometric mean = √(16×8) = √128 = √(64×2) = 8√2 ✔

But look at options:

A. 64
B. 8√2
C. 8
D. √32

We got x = 8 → that’s option C.

But wait — let me double-check the question:
“8√2 is the geometric mean of 16 and what other number?”

Yes, we solved: √(16x) = 8√2 → square both sides → 16x = 128 → x=8.

✔ So answer is C. 8

*(Note: Option B is 8√2 — that’s the geometric mean itself, not the missing number.)*

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Question 6: In the right triangle with altitude to hypotenuse, segments are 12 and 8. Find x (the altitude).

In a right triangle, when you draw an altitude from the right angle to the hypotenuse, it creates two smaller similar triangles.

The key rule:
Altitude squared = product of the two segments of the hypotenuse

So:
x² = 12 × 8 = 96
→ x = √96

Simplify √96:
96 = 16 × 6 → √(16×6) = 4√6

Check options:

A. √6
B. 2
C. 4√6
D. 6√4 → which is 6×2=12, too big

✔ Answer: C. 4√6

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Final Answers:

1. B
2. C
3. B
4. B
5. C
6. C