$\left(1+\sqrt{3}\right)^2 - \left(1-\sqrt{3}\right)^2$ is :

Question

Accepted Answer

## Model Answer $(1+\sqrt{3})^2 - (1-\sqrt{3})^2 = (1+3+2\sqrt{3}) - (1+3-2\sqrt{3}) = 4\sqrt{3}$, which is a positive irrational number. **(c) a positive irrational number.** ## Explanation Use the identity $a^2 - b^2 = (a+b)(a-b)$ or expand directly. The rational parts cancel, leaving $4\sqrt{3}$ — a positive irrational (product of a non-zero rational and an irrational).

Mathematics — Standard (041) — CBSE Class 10 board question