Estimating Square Roots

Estimating Square Roots

Use your understanding of perfect square numbers and their square roots to estimate non-perfect square numbers.

Estimating Square Roots

Determine which two integers the evaluated square root would be between. Perfect square numbers will help you to estimate.

Multiple Choice

What two integers is  $\sqrt{5}$  between?

• 3 & 4

• 1 & 2

• 0 & 1

• 2 & 3

 $\sqrt{5}$  would land between  $\sqrt{4}$  and  $\sqrt{9}$  

So the integers would be between 2 & 3.

Notice where it lands in between.

Its closer to the integer 2 because

 $\sqrt{5}$  is closer to  $\sqrt{4}$  

Multiple Choice

What two integers is  $-\sqrt{17}$  between?

• -16 & -17

• -4 & -5

• -3 & -4

• -5 & -6

 $-\sqrt{17}$  would land between  $-\sqrt{16}$  and  $-\sqrt{25}$  

So the integers would be between -4 & -5.

Notice where it lands in between.

Its closer to the integer -4 because

 $-\sqrt{17}$  is closer to  $-\sqrt{16}$  

Multiple Choice

What two integers is  $\sqrt{89}$  between?

• 85 & 90

• 7 & 8

• 8 & 9

• 9 & 10

 $\sqrt{89}$  is between  $\sqrt{81}$  &  $\sqrt{100}$  

So the integers were 9 & 10

Multiple Choice

What two integers is  $\sqrt{250}$  between?

• 15 & 16

• 16 & 17

• 18 & 19

• 14 & 15

 $\sqrt{250}$  is between  $\sqrt{225}$  &  $\sqrt{256}$  

So the integers were 15 & 16

Multiple Choice

What two integers is  $\sqrt{150}$  between?

• 10 & 11

• 11 & 12

• 12 & 13

• 13 & 14

 $\sqrt{150}$  is between  $\sqrt{144}$  &  $\sqrt{169}$  

So the integers were 12 & 13

Let's try some fill in the blanks.

Switch it up a little.

Fill in the Blank

What two integers is  $\sqrt{75}$  between?

Fill in the Blank

What two integers is  $\sqrt{389}$  between?

Fill in the Blank

What two integers is  $-\sqrt{47}$  between?

Poll

On a scale of 1 to 5, how do you feel about estimating square roots?

• 5 (I understand it perfectly)

• 4 (I understand it pretty well)

• 3 (I think I get it but I need a little more practice)

• 2 (I kind of get it a little)

• 1 (I have no idea)

Open Ended

Explain in your own words, how do you estimate the integers the square root lands between?