Surds & Indices: Complete Learning Suite

Zero to Hero 🚀

Surds & Indices: The Complete Archive

Theory + Basic Worksheet + 150 Titan Problems

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The Rule Book (Read First)

A. Laws of Indices (The Power Rules)

1. Multiplication Rule

If bases are same, ADD the powers.

$$ a^m \times a^n = a^{m+n} $$

2. Division Rule

If bases are same, SUBTRACT the powers.

$$ \frac{a^m}{a^n} = a^{m-n} $$

3. Power of Power

MULTIPLY the powers.

$$ (a^m)^n = a^{m \times n} $$

4. Zero & Negative Rule

Zero power is 1. Negative power flips the fraction.

$$ a^0 = 1 \quad | \quad a^{-n} = \frac{1}{a^n} $$

B. Laws of Surds (The Root Rules)

Addition $$ 2\sqrt{3} + 5\sqrt{3} = 7\sqrt{3} $$
Multiplication $$ \sqrt{a} \times \sqrt{b} = \sqrt{ab} $$
Rationalization $$ \frac{1}{\sqrt{a}} \times \frac{\sqrt{a}}{\sqrt{a}} = \frac{\sqrt{a}}{a} $$

C. The Toolkit: Identities

$(a+b)^2 = a^2+b^2+2ab$
$(a-b)^2 = a^2+b^2-2ab$
$a^2-b^2 = (a+b)(a-b)$
$\sqrt{2} \approx 1.414$
$\sqrt{3} \approx 1.732$
$\sqrt{5} \approx 2.236$

Warm-Up Zone

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Titan Gauntlet: Phase I

II

The Titan Vault (100 New Challenges)

Pure Adrenaline for Math Athletes

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