Question

Writing On a number line, between which two consecutive whole numbers would √221 be located? Use pencil and paper Explain why it might be used to approximate the value rather than use the exact value.​

Answer 1

√221 is between 14 and 15.

√221 ≈ 14.86

Explanation:

Perfect square: A number made by squaring a whole number.

Perfect squares: 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:

`\implies \sf √(196) < √(221) < √(225)`

`\implies \sf √(14^2) < √(221) < √(15^2)`

`\implies \sf 14 < √(221) < 15`

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. 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.