Square Roots and Irrational Numbers

Estimating Irrational Numbers- Part 2

I can estimate irrational numbers by approximating their location on a number line or by truncating their decimal expansions.

Ensure you watch the video in order to learn how to do the examples! This will also help with your Homework.

Estimate a square root to the nearest tenth

• First- Start with what square root the number is between and then which is closest to the number

• Second- Start doing trials to see which number squared is closest to the number

• Last- Estimate which number it is

Example²

• Find the square root of 15 to the nearest tenth.

• First- The square root of 15 is between the square root of 9 and 16.

• Second- The square root of 15 is closest to 16

• Third- We start trials. We can start with 3.8 and 3.9. 3.8²=14.44 and 3.9²=15.21.

• Fourth- We see that 15 is closer to 3.9 so the answer is approximately 3.9.

Multiple Choice

What does truncating mean?

• To round the decimal

• To take away part of the decimal

• To cut all the decimal off, but keep the whole number

Multiple Choice

Estimate the cubed root of 32 to the nearest integer

• 3

• 4

• 5

• 6

Multiple Choice

Estimate the cubed root of 200 to the nearest integer

• 4

• 5

• 6

• 7

Multiple Choice

Estimate the cubed root of 3 to the nearest integer

• 1

• 2

• 3

• 4

Multiple Choice

Estimate the square root of 270 to the nearest tenth

• 16.1

• 16.2

• 16.3

• 16.4

Multiple Choice

Estimate the square root of 52 to the nearest tenth

• 6.9

• 7

• 7.1

• 7.2

Multiple Choice

The radius of a circle is square root of 15m inches. Truncate the value of the square root of 15m when

m = 3, to the tenths place.

• 7.4

• 1.8

• 6.7

• 5.7

Multiple Choice

The formula D= the square root of x²+36 can be used to find the distance D between two points. Truncate the value of the square root of x²+36 when x=6, to the tenths place.

• 16.2

• 8.4

• 13.4

• 2.2

Multiple Choice

Estimate the square root of 152 to the nearest integer

• 12

• 13

• 10

• 11

Multiple Select

Name the set(s) the square root of 2 belongs to.

• rational

• irrational

• whole

• integer

• natural

Poll

How do you feel about irrational and rational numbers?

• Great!

• Not Great!

• So-So