Question
The positive square root of $7+\sqrt{48},$ is:
✓
Answer
- $2+\sqrt3$
Solution:
$\sqrt{7+\sqrt{48}}$
$=\sqrt{7+2\sqrt{12}}$
$=\sqrt{4+3+2\sqrt4\times\sqrt3}$
$=\sqrt{\big(\sqrt4\big)^2+\big(\sqrt3\big)^2+2\times\sqrt4\times\sqrt3}$
$=\sqrt{\big(\sqrt4+\sqrt3\big)^2}$
$=\pm\big(\sqrt4+\sqrt3\big)$
Positive value is $\sqrt4+\sqrt3=2+\sqrt3$
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
If $\text{x}+\frac{1}{\text{x}}=3,$ then $\text{x}^6+\frac{1}{\text{x}^6}=$
→The base of an isosceles triangle is 8cm long and each of its equal sides measures 6cm. The area of the triangle is:
Write the correct answer in the following:
Decimal representation of a rational number cannot be.
Decimal representation of a rational number cannot be.
- Terminating.
- Non - terminating.
- Non - terminating repeating.
- Non - terminating non - repeating.
When the data consists of 3, 4, 5, 4, 3, 4, 5, which statement is true?
The value of $\sqrt{5+2\sqrt6},$ is:
→- $\sqrt3-\sqrt2$
- $\sqrt3+\sqrt2$
- $\sqrt5+\sqrt6$
- None of these
Write the correct answer in the following:
The value of 1.999... in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0,$ is
→The value of 1.999... in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0,$ is
Write the correct answer in the following:
The product of any two irrational numbers is.
The product of any two irrational numbers is.
In the given figure, O is the centre of a circle. If $\angle\text{OAC}=50^\circ$ then $\angle\text{ODB}=?$
→