MCQ
If $\sqrt2=1.4142,$ then $\sqrt{\frac{\sqrt2-1}{\sqrt2+1}}$ is equal to:
- A0.1718
- B5.8282
- C0.4142
- D2.4142
✓
Answer
- 0.4142
Solution:
By Rationalising $\frac{\sqrt2-1}{\sqrt2+1},$ we get
$\frac{\sqrt2-1}{\sqrt2+1}\times\frac{\sqrt2-1}{\sqrt2-1}=\frac{\big(\sqrt2-1\big)^2}{\big(\sqrt2\big)^2-1^2}=\frac{\big(\sqrt2-1\big)^2}{1}$
So $\sqrt{\frac{\sqrt2-1}{\sqrt2+1}}=\sqrt{\frac{\big(\sqrt2-1\big)^2}{1}}\\ \ =\big(\sqrt2-1\big)=1.4142-1=0.4142$
Hence, correct option is (c).
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The remainder when $f(x)=x^5$ is divided by $g(x)=x^2-9$, is
→The distance between the graphs of the equations y = -1 and y = 3 is:
- 2
- 4
- 3
- 1
An ice cream cone has hemispherical top. If the height of the cone is 9cm and base radius is 2.5cm, then the volume of ice cream is:
The area of the Fig. formed by joining points $A(-1,5)$ and $B(-2,4)$ and their reflections in $u$-axis is
→A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
The curved surface area of a right circular cylinder which just encloses a sphere of radius r is:
If we divide both sides of a linear equation with a non-zero number, then the solution of the linear equation.
The graph of the linear equation 4x + 2y = 12, cuts the x-axis at the point:
Write the correct answer in the following:
In coordinates of P are:
In coordinates of P are:
- (-4, 2)
- (-2, 4)
- (4, -2)
- (2, -4)
In a $\triangle\text{ABC}, \ \angle\text{A} = 50^\circ$ and BC is produced to a point D. If the bisectors $\angle\text{ACD}$ meet at E, then $\angle\text{E} =$
→