MCQ
The number $(\sqrt{3}+\sqrt{5})^2$ is :
- Aan integer
- Bnot a real number
- ✓an irrational number
- Da rational number
✓
Answer
Correct option: C.
an irrational number
$\big(\sqrt{3}+\sqrt{5}\big)^2$
$=\big(\sqrt{3}\big)^2+\big(\sqrt{5} \big)^2+2\times\sqrt{3}\times\sqrt{5}$
$= 3 + 5 + 2\sqrt{15}$
$=8+2\sqrt{15}$
Here, $\sqrt{15}=\sqrt{3}\times\sqrt{5}$
Since $\sqrt{3}$ and $\sqrt{5}$ both are an irrational number.
Therefore, $\big(\sqrt{3}+\sqrt{5}\big)^2$ is an irrational number.
$=\big(\sqrt{3}\big)^2+\big(\sqrt{5} \big)^2+2\times\sqrt{3}\times\sqrt{5}$
$= 3 + 5 + 2\sqrt{15}$
$=8+2\sqrt{15}$
Here, $\sqrt{15}=\sqrt{3}\times\sqrt{5}$
Since $\sqrt{3}$ and $\sqrt{5}$ both are an irrational number.
Therefore, $\big(\sqrt{3}+\sqrt{5}\big)^2$ is an irrational number.
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