**20cm**

**²**

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:**

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