Question

Given√2=1•414, find to three places of decimals the values of 1+√2/3-2√2​

Answer 1

Answer:

14.070

Solution:

Here,

We need to find the value of (1+√2)/(3-2√2) upto three places of decimals , given that √2 = 1.414 .

Thus,

(1 + √2) / (3 - 2√2)

= (1 + √2)(3 + 2√2) / (3 - 2√2)(3 + 2√2)

= (3 + 2√2 + 3√2 + 4) / [ 3² - (2√2)² ]

= (7 + 5√2) / (9 - 8)

= (7 + 5√2) / 1

= 7 + 5√2

= 7 + 5×1.414

= 7 + 7.070

= 14.070

Hence,

Required answer is 14.070