Answered By Albert S

In decimal form the two numbers are 0.5 and 109.5. The way they are trying to puzzle you is with the perfect square aspect. A perfect square is the product of a rational number and itself. Rational numbers are 1,2,3,4 ... Without the understanding of 'perfect square' a person might go into decimals to find an answer for the first number in question but we don't need to do this -we are working with the whole numbers not fractions. The perfect square closest to 5/10=0.5 are 1 and 4 the sqare roots of 1 is 1. The square root of 4 is 2.

For 109.5 the close perfect squares are 81, 100, 121, 144. The closest perfect squares are 100 and 121. The sqare root of 100 is 10, the square root of 121 is 11. 

Answered By Emily H

To solve this problem, you should start by writing the values they give you in decimal form, which in this case become 0.5 and 109.5.

What this question is effectively asking you to do is to find two whole numbers which when squared form an interval around the value in question.To that end, you may find it helpful to list all perfect squares until you find one larger than the larger of your two values:

  $\left\{0,1,2,4,9,16,25,36,49,64,81,100,121,...\right\}${0,1,2,4,9,16,25,36,49,64,81,100,121,...} 

Then with this list, it becomes a simple matter to see find your answer:

  $\sqrt{0}<\sqrt{0.5}<\sqrt{1}$√0<√0.5<√1

   $0<\sqrt{0.5}<1$0<√0.5<1 

AND

 $\sqrt{100}<\sqrt{109.5}<\sqrt{121}$√100<√109.5<√121 

   $10<\sqrt{109.5}<11$10<√109.5<11

Answered By Xuezhong J

For Question 2, the answer is clear,    100 and 121,  their roots are 10 and 11.

But for question 1,   it's tricky,  0 is considered as a perfect square or not? 

If it is, then the answer is 0 and 4, their roots are 0 and 1.

If it's not, then the answer is 1 and 4, their roots is 1 and 2.