Find the value of √5 correct to two places of decimal.
We know that 22 = 4 < 5 < 9 = 32
Taking positive square roots we get
2 <√5 < 3.
Next, (2.2)2 = 4.84 < 5 < 5.29 = (2.3)2
Taking positive square roots, we have
2.2 <√5 < 2.3
Again, (2.23)2 = 4.9729< 5< 5.0176 = ( 2.24)2
Taking positive square roots, we obtain
2.23 <√5 < 2.24
Hence the required approximation is 2.24 as (2.24)2 is nearest to 5 than (2.23)2 .
Taking positive square roots we get
2 <√5 < 3.
Next, (2.2)2 = 4.84 < 5 < 5.29 = (2.3)2
Taking positive square roots, we have
2.2 <√5 < 2.3
Again, (2.23)2 = 4.9729< 5< 5.0176 = ( 2.24)2
Taking positive square roots, we obtain
2.23 <√5 < 2.24
Hence the required approximation is 2.24 as (2.24)2 is nearest to 5 than (2.23)2 .
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
= a + b
= a + b