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## Sunday, February 5, 2012

### Anita's Square Root Post

11) The square root has an area of 20cm²

a) Use perfect squares to estimate the side length to one decimal place.
b) Check your answer using a ruler to measure the side of the square. Measure to the nearest tenth of a centimeter.

Solution:

Step 1: Make a number line putting the closest perfect square lesser than the number to the left, then placing the closest perfect square of greater value than the given number to the right.

Step 2: On the number line shown, 16 is the square root of 4, and 25 is the square root of 5. The number (20) is closer to 16, so we place 20 slightly to the left of the median number.

Step 3: Count how many times the lesser number (16) has to move to become 20, which is four times. Now you add a '4' to the tenths place behind the whole number. The square root of 20 is approximately 4.4 .

14) Alex is thinking of a number:
The number has a square root between 7 and 8, and it is a multiple of 12.

a) What number could he be thinking of?

Solution:

Square root of 7: 49
Square root of 8: 64
Numbers in between 49 and 64: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63.
Multiples of 12: 60.

b) Is there more than one answer? Explain.
No, there cannot be more than one answer.

15) Order the following numbers from least to greatest:

Solution: find all the square roots of 46 and 27 to make ordering them from least to greatest easier.

Least to greatest: