Question

ifroot2 =1.414 then ​

Answer 1

Answer:

by rationalisation

we get

√(√2-1) ^2/1

=√2-1

put value of √2

answer is 1.414-1

=0.414

ok

follow me

dudes

Answer 2

$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Question}}}}}{\bigstar}$

□☆□☆□☆□☆□☆□☆□☆□☆□☆□

$If \ \sqrt2 = 1.414 ,\ evaluate : \ \displaystyle \sqrt{ \frac{\sqrt2 - 1}{\sqrt2 +1}}$

□☆□☆□☆□☆□☆□☆□☆□☆□☆□

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Answer}}}}}{\bigstar}$

$\boxed{\red{\bold{Evaluating:}}}$

$\purple{\implies \displaystyle \sqrt{ \frac{\sqrt2-1}{\sqrt2+1}}}$

$\boxed{\red{\bold{Rationalizing:}}}$

$\red{\implies}\displaystyle \sqrt{ \frac{\sqrt2-1}{\sqrt2+1} \times \frac{\sqrt2-1}{\sqrt2-1}}$

$\red{\implies}\displaystyle \sqrt{ \frac{(\sqrt2-1)^2}{\sqrt2^2 - 1^2}}$

$\red{\implies}\displaystyle \sqrt{ \frac{(\sqrt2-1)^2}{2-1}}$

$\red{\implies}\displaystyle \sqrt{(\sqrt2-1)^2}$

$\red{\implies}\sqrt2 - 1$

$\boxed{\red{\bold{Putting \ \sqrt2 = 1.414:}}}$

$\green{\implies 1.414 - 1}$

$\green{\boxed{\implies{\boxed{0.414}}}}$

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂