Maths

SSC CGL Maths Chapter 3: Indices and Surds – Smart Tricks & Fast Calculation Guide

SSC CGL Maths Chapter 3: Indices and Surds: Mastering Indices and Surds is essential for scoring high in the SSC CGL exam. Though it might seem tricky at first, this chapter becomes super easy once you understand the rules and practice with the right approach. In this post, we’ll cover the basic concepts, shortcut tricks, key formulas, and practice examples that will make solving these questions a breeze!

Table of Contents

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🔍 What You’ll Learn in Chapter 3:

Meaning of Indices (Powers)
Laws of Indices with Examples
Understanding Surds (Irrational Roots)
Simplifying Surds Easily
SSC CGL Exam Patterns
Practice Questions with Short Tricks

📖 Basic Concepts:

✅ What are Indices?

Indices (also called powers or exponents) represent how many times a number is multiplied by itself.
📌 Example:
$23=2×2×2=82^3 = 2 \times 2 \times 2 = 8$

✅ What are Surds?

A surd is an irrational number which cannot be simplified to remove the root.
📌 Example:
$2,3,5\sqrt{2}, \sqrt{3}, \sqrt{5}$ are surds because they can’t be expressed as exact fractions.

🧠 Important Laws of Indices:

Law	Rule	Example
1	$am×an=am+na^m \times a^n = a^{m+n}$	$23×22=25=322^3 \times 2^2 = 2^5 = 32$
2	$aman=am−n\frac{a^m}{a^n} = a^{m-n}$	$5^4 / 5^2 = 5^2 = 25$
3	$a^m)^n = a^{mn}$	$3^2)^3 = 3^6 = 729$
4	$a^0 = 1$	$7^0 = 1$
5	$a^{-n} = 1/a^n$	$2^{-3} = 1/8$

🧮 Surds Simplification Tricks:

$a×b=a×b\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$
$ab=a/b\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{a/b}$
Multiply and rationalize the denominator using conjugates if needed.

📌 Example:
$50=25×2=52\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$

⚡ Pro Tips to Solve Faster:

✅ Learn the Laws by Heart – They save time in every question
✅ Practice Simplification Daily – Especially with surds like $72\sqrt{72}$
✅ Remember Common Surd Values – Like $2≈1.41\sqrt{2} \approx 1.41$ , $3≈1.73\sqrt{3} \approx 1.73$