PCTB 2025–26Punjab Board Class 9 Mathematics — new 2025/26 syllabus, free and live.

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Q #2 Part (v)PCTB Class 9 • Real Numbers • Ex 1.2

Teacher Verified • PCTB 2025–26

Question Statement

Simplify the following algebraic radical expression:

\frac{5 \cdot (25)^{n + 1} - 25 \cdot (5)^{2 n}}{5 \cdot (5)^{2 n + 3} - (25)^{n + 1}}

Key Concept & Rules

Convert all bases to prime base

5

25 = 5^{2} ⟹ (25)^{n + 1} = 5^{2 n + 2}

. Factor out common monomial

5^{2 n + 2}

Step 1 — Express all terms with prime base 5:

Numerator: 5^{1} \cdot 5^{2 n + 2} - 5^{2 n + 2} = 5^{2 n + 2} (5 - 1) = 5^{2 n + 2} (4)

Denominator: 5^{2 n + 4} - 5^{2 n + 2} = 5^{2 n + 2} (5^{2} - 1) = 5^{2 n + 2} (24)

Step 2 — Cancel common factors and reduce fraction:

\frac{5^{2 n + 2} \cdot 4}{5^{2 n + 2} \cdot 24} = \frac{4}{24} = \frac{𝟏}{𝟔}

Final Boxed Answer:1 / 6

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Q.3 Solve

x^{2} - 5 x + 6 = 0

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

where

a = 1

b = - 5

c = 6

x = 3 or x = 2

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