Question

find the value of square root of 3.1428 and square root of 0.31428 correct to 3 decimal places ​

Answer 1

Answer:

324=18²

Let 314.28=(18-Δ)²=324–36Δ+Δ²

36Δ≈9.72

Δ≈9.72/36=0.27

∴first approximation for

√314.28=18–0.27=17.73

√3.142≈1.77

(1.77)²=

=(1.8–0.03)²

=3.240–0.108+0.009

=3.1329 <3.1428

(17.7+Δ)²=313.29+35.4Δ+Δ²

35.4Δ≈314.28-313.29=0.99

Δ≈0.99/35.4≈0.01×990/354≈0.028

2nd approximation for

√314.28=17.7+0.028=17.728

√3.1428=1.7728≈1.773 (3dp)

②55²= 3025

56²=(55+1)²=3025+110+1=3136

Let 3142.8=(56-Δ)²=3136–112Δ+Δ²

112Δ≈3142.8-3136=6.8

112Δ≈6.8

Δ≈6.8/112=0.01×680/112≈0.0607

∴56–0.0607=55.94

0.5594≈0.559 (3dp) is good enough

as an approximation for √0.31428

Answer 2

Answer:

The square root of 3.1428 is 1.77 and that of 0.31428 is 0.56