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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

5. Irrational Numbers

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Exercise 51 Page 408

Make a table of decimal numbers whose squares are close to 1.52.

1.2

Practice makes perfect

We are asked to approximate sqrt(1.52) to the nearest tenth. This number must be approximated rather than evaluated because it is an irrational number.

Irrational Number
A number that cannot be written as ab, where a and b are integers and b is not zero.

Let's start by making a table of decimal numbers between 1 and 2 whose squares are close to 1.52.

Number	Square of Number
1	1^2=1
1.1	1.1^2=1.21
1.2	1.2^2= 1.44
1.3	1.3^2= 1.69

The table shows that 1.52 is between 1.44 and 1.69. Because 1.52 is closer to 1.44 than to 1.69, we can say that sqrt(1.52) is closer to sqrt(1.44) than to sqrt(1.69). This means that sqrt(1.52) is closer to 1.2 than to 1.3.

number line

We have that sqrt(1.52) is approximately 1.2.

Subchapter links

Try It p.402-404

Self-Assessment for Concepts & Skills p.404

Self-Assessment for Problem Solving p.405

Review & Refresh p.406

Concepts, Skills, & Problem Solving p.406-408