1. 7.4 Approximating Square Roots
Essential Question: How can you find decimal approximations of square roots that are not rational?

2. List the integers each is between
𝟏. 𝟐𝟕𝟔 𝒊𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 ________ & ________
𝟔𝟏 𝒊𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 ________ & ________
𝟏𝟖𝟕 𝒊𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 ________ & ________
𝟏𝟓𝟓 𝒊𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 ________ & ________
6. 𝟐 𝒊𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 ________ & ________
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3. 238 256 225 238 is a little less than half way between 15 & 15.5
Approximate (a) to the nearest integer & (b) to the nearest tenth:
238
256
225
is a little less than half way between 15 & 15.5
Approximately 15.4
238

4. 141
Approximate (a) to the nearest integer & (b) to the nearest tenth:

5. Approximating to the tenths’ place Method 2

6. Approximate to the nearest tenth.
Step 1: Find the perfect squares above & below.
Step 2: Subtract original and lower radicals.
141 – 121 = 20
Step 3: Subtract lower and higher radicals.
144 – 121 = 23
Step 4: Write as a fraction
These are the mathematical steps…We do not have to go to this detail. Use top slides and estimate instead 20 23
Step 5: Divide fraction to write as a decimal
20  23 ≈ 0.86 round to the nearest tenth of a decimal ≈.9
Step 6: add lower perfect square integer & decimal
11+.9=11.9

7. On your own practice:
Approximate (a) to the nearest integer & (b) to the nearest tenth:
150 7

8. Approximate (a) to the nearest integer & (b) to the nearest tenth:

9. Is this a reasonable approximation 23 , 112 5
Is this a reasonable approximation 23 , ? Which is greater, 10 𝑜𝑟 5 ? Which is greater, −2 𝑜𝑟 − 2 ?

11. Leave this side open for corrections.
Name
Date
Period
7.4 pg 313 #2, 6, evens, 46, 48
Leave this side open for corrections.