Question

if √2= 1.414 then solve under root √2-1/√2+1​

Answer 1

Step-by-step explanation:

The given fraction is an irrational one. To rationalize it, we have to multiply its numerator and denominator by a factor which will give a rational product with a rational denominator. Towards this end, we multiply the numerator and the denominator of the given expression by √(√2 - 1) and write,

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

= [√(√ 2 - 1) x √(√ 2 - 1)] / [√(√ 2 + 1) √(√ 2 - 1)] = (√ 2 - 1) / √[(√ 2 + 1)(√ 2 - 1)]

=(√ 2 - 1) / √[(√2)² - 1² )] = (√2 - 1)/√(2 - 1) = (√2 - 1)/√1 = (√2 - 1)/1 = √2 - 1 (Considering only the positive root).

= 1.4142 - 1 = 0.4142, to 4 decimal figures.

Answer 2

$\frac{ \sqrt{2 - 1} }{ \sqrt{2 + 1} } = \frac{ \sqrt{1} }{ \sqrt{3} } = \frac{1}{1.73} answer.$