Square Root — O/L Mathematics

What must I remember about Square Root?

• Square root definition: If x² = y, then x is the square root of y (x = √y); positive square root is the principal root.
• Square root by prime factorization: Express the number as a product of prime factors in index notation; half each exponent to obtain the square root (e.g., √576 = √(2⁶ × 3²) = 2³ × 3¹ = 24).
• Division method for square root: Group digits in pairs starting from the decimal point moving left for whole numbers and right for decimals; find largest digit whose square is ≤ current group.
• Approximating square roots of non-perfect squares: Identify nearest perfect squares bounding the number (e.g., for √14: 9 < 14 < 16, so 3 < √14 < 4; linear interpolation gives √14 ≈ 3.7).

Test yourself (1 minute)

1. Digit pairing rule

   Grouping MUST start from the decimal point: whole numbers paired right-to-left (e.g., 1,44.00), decimals paired left-to-right (e.g., 0.05,20).

2. Decimal place precision

   To find square root correct to 2 decimal places, continue division until 3 decimal digits are obtained, then round appropriately.

3. Square root of fractions

   √(a/b) = √a / √b; if denominator is not a perfect square, rationalize denominator first: √(a/b) = √(ab) / b.

Practise Square Root questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 2)

What should I study first?

What comes next?

Next in the syllabus

Where does Square Root fit in the syllabus?

Grade 10 · Term 1