📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
$\left(1+\sqrt{3}\right)^2 - \left(1-\sqrt{3}\right)^2$ is :
  1. (a) a positive rational number.
  2. (b) a negative integer.
  3. (c) a positive irrational number.
  4. (d) a negative irrational number.
Previously asked in CBSE board exam
2025 30/4/1 Q2
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
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).

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.