G8

Grade 8 Unit 1 Lesson 7 P TE

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Challenge Problems

Directions: Solve.

1. 
   

   Is (^2) √ 4 the same as (^4) √ 2? Why or why
   not?
   Solution:
   No, they are not equal. (^2) √ 4 simplifies to 2(2) = 4. We
   know that √ 2 is greater than √ 1 because 2 is greater
   than 1, thus 4 √ 2 will be 4 times some number greater
   than 1, which will not equal 4. Thus, the two are not
   equal.

   
   


2. 
   

   Find an irrational number whose decimal
   approximation is between 15 and 16. What
   process did you use?

   
   

Solution:

The square root of a number between 225 and 256 is

irrational. The approximate square root will fall

between 15 and 16. I multiplied 15 x 15 = 225 and 16 x 16

=256.

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.

* MP4: Apply mathematics in everyday life.

Directions: Using the digits 0-9, fill in the boxes so that the square root falls either on or in

between the indicated number(s) on the number line.

4 5 6 7 8 9

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