Answer:
√221 is between 14 and 15.
√221 ≈ 14.86
Step-by-step explanation:
Perfect square: Â A number made by squaring a whole number.
Perfect squares: Â 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ...
To find an approximate value of a square root, find the perfect squares above and below the number:
⇒ 196 < 221 < 225
Therefore:
[tex]\implies \sf \sqrt{196} < \sqrt{221} < \sqrt{225}[/tex]
[tex]\implies \sf \sqrt{14^2} < \sqrt{221} < \sqrt{15^2}[/tex]
[tex]\implies \sf 14 < \sqrt{221} < 15[/tex]
Therefore, √221 is between 14 and 15 on a number line.
Drawing the number line
- Draw a number line from 196 to 225.
- Place 14 below 196 and 15 below 225.
- Divide the space between 14 and 15 into 10 equal increments.
(see attachment 1)
Locate 221 on the number line. We can see that it is between 14.8 and 14.9. Â Place a marker halfway between 14.8 and 14.9, then divide the second half into 5 equal increments (see attachment 2).
Therefore, an approx value of √221 is 14.86.
