Step 1: Find the whole number of the decimal form of √6 by perfect square method.
The largest perfect square less than 6 is 4.
The smallest perfect square greater than 6 is 9.
4 < 6 < 9
√4 < √6 < √9
2 < √6 < 3
∴ The whole number of decimal form of √6 lies between 2 and 3.
√6 = 2._____
Step 2: Then, find the first decimal place of the decimal form of √6 by perfect square method. So, consider 600.
The largest perfect square less than 600 is 576.
The smallest perfect square greater than 6 is 625.
576 < 600 < 625
242 < 600 < 252 (∵242=576;252=625)
Now place the decimal point
5.76 < 6.00 < 6.25
2.42 < 6 < 2.52
√2.42 < √6 < √2.52
2.4 < √6 <2.5
∴ The first decimal place of √6 is 4.
√6 = 2.4
Step 3: Then, find the second decimal place of the decimal form of √6 by perfect square method. So, consider 60,000.
The largest perfect square less than 60,000 is 59,536.
The smallest perfect square greater than 6 is 60,025.
59,536 < 60,000 < 60,025
2442 < 60,000 < 2452
(∵2442=59,536;2452=60,025)
Now place the decimal point
5.9536 < 6.0000 < 6.0025
2.442 < 6.0000 < 2.452
√2.442 < √6 < √2.452
2.44 < √6 <2.45
∴ The second decimal place of √6 is 4.
So we can write √6 as 2.44 .
∴ The approximate value of √6 is 2.44.