If -2-1-414- then-2-1-2-1- a 0-207 b 2-414 c 0-414 d 0-621

√(2)=1.414 (√(2) 1)/(√(2)+1)= (√(2) 1)(√(2) 1)/(√(2)+1)(√(2) 1) = (√(2) 1)^2/(2 1) =(√(2) 1)^2 √((√(2) 1)/(√(2)+1)) = √((√(2) 1)^2) = √(2) 1 = 1.414 1 = 0.4 ...

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Byju's Answer

Standard IX

Mathematics

Operations on Rational and Irrational Numbers

If √2=1.414 ...

Question

If $\sqrt{2} = 1.414 t h e n \sqrt{\frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)}} = ?$

(a) 0.207 (b) 2.414 (c) 0.414 (d) 0.621

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Solution

$\sqrt{2} = 1.414 \frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)} = \frac{(\sqrt{2} - 1) (\sqrt{2} - 1)}{(\sqrt{2} + 1) (\sqrt{2} - 1)} = \frac{(\sqrt{2} - 1)^{2}}{(2 - 1)} = (\sqrt{2} - 1)^{2} \sqrt{\frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)}} = \sqrt{(\sqrt{2} - 1)^{2}} = \sqrt{2} - 1 = 1.414 - 1 = 0.414$

Hence, the correct answer is option (c).

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Similar questions

Q. If

\sqrt{2} = 1.414

, then

\sqrt{\frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)}}

=?
(a) 0.207
(b) 2.414
(c) 0.414
(d) 0.621

Q. If

\sqrt{2} = 1.414 then \sqrt{\frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)}} = ?

(a) 0.207
(b) 2.414
(c) 0.414
(d) 0.621

Q. If

\sqrt{2} = 1.414

, then find the value of

\frac{1}{1 - \sqrt{2}}

If $\sqrt{2} = 1.414, t h e n \sqrt{\frac{\sqrt{2} - 1}{(\sqrt{2} + 1)}} =$ ?

Q. If

\sqrt{2} = 1.414,

then the value of

\sqrt{6} - \sqrt{3}

upto three places of decimal is

(a) 0.235

(b) 0.707

(c) 1.414

(d) 0.471

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If √2=1.414 then √(√2−1)(√2+1)=? (a) 0.207 (b) 2.414 (c) 0.414 (d) 0.621

√2=1.414(√2−1)(√2+1)=(√2−1)(√2−1)(√2+1)(√2−1)=(√2−1)2(2−1)=(√2−1)2√(√2−1)(√2+1)=√(√2−1)2=√2−1=1.414−1=0.414 Hence, the correct answer is option (c).

If $\sqrt{2} = 1.414 t h e n \sqrt{\frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)}} = ?$

(a) 0.207 (b) 2.414 (c) 0.414 (d) 0.621