Intermediate Test Prep (Grades7-8) More on Square Roots

From our perfect squares lesson we learned that when we square a whole number, or multiply it by itself, our product is a perfect square.

If we take the square root of a perfect square we would get the original factor as the answer.

Example:

	because 6x6=36
	because 8x8=64
	because 10x10=100

Whole numbers that are not perfect squares still have square roots. However, their square roots are not whole numbers, they are decimals or fractional parts of whole numbers.

For the purpose of this lesson we will simply tell which two consecutive whole numbers the square root of a whole number is between.

Consecutive Whole Numbers: Two whole numbers that follow each other in order on a number line (i.e. 6 and 7).

Example 1: Between what two consecutive whole numbers is

Solution: Think about our list of perfect squares:

0,1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Since 153 is between 144 and 169 in our perfect squares list, the square root of 153 is between 12 and 13 (12 and 13 are the square roots of 144 and 169).

Example 2: Between what two consecutive whole numbers is the square root of 17?

Solution: Since 17 is between 16 and 25 in our perfect squares list, the square root of 17 must be between 4 and 5.

Example 3: Between what two consecutive whole numbers is

Solution: Since 200 is between 196 and 225 in our perfect squares list, the square root of 200 is between 14 and 15.

Remember:

Use your perfect square list to find the square roots of all numbers!