Mathematics · 2nd preparatory · First Term

Numbers and Their Operations — Laws of Square and Cube Roots

About this lesson

This unit teaches the laws of multiplication and division of square roots and cube roots. Students learn to simplify radical expressions by factoring out perfect squares or perfect cubes, rationalizing denominators, and combining like radical terms. The unit includes worked examples, self-evaluation exercises, and real-life geometry problems involving perimeters and areas of squares and rectangles, such as finding the side length of a square given its area or the length of a fence around a seedbed. By the end, students should be able to apply these laws to simplify numerical expressions and solve practical problems.

Main topics in this lesson

  • Laws of square roots
  • Laws of cube roots
  • Simplifying radical expressions
  • Rationalizing denominators
  • Real-life applications of roots

Key terms and vocabulary

  • Square root
  • Cube root
  • Perfect square
  • Perfect cube
  • Rationalizing the denominator

Questions and answers on Numbers and Their Operations — Laws of Square and Cube Roots - practice and revision

Multiple choice questions on this lesson in Mathematics for 2nd preparatory, First Term, with practice exercises for revision and exam preparation.

1

حوض على شكل مربع مساحته ١٢٨ سم². ما طول ضلعه في أبسط صورة؟

  • 1 ٨√٢ سم
  • 2 ٢√٨ سم
  • 3 ١٦ سم
  • 4 ٦٤√٢ سم
2

مساحة مربع تساوي ٧٥ سم². ما طول ضلعه في أبسط صورة؟

  • 1 ٥√٣ سم
  • 2 ٣√٥ سم
  • 3 ١٥ سم
  • 4 ٢٥√٣ سم
3

مساحة مربع تساوي ٩٨ سم². ما طول ضلعه في أبسط صورة؟

  • 1 ٧√٢ سم
  • 2 ٢√٧ سم
  • 3 ١٤ سم
  • 4 ٤٩√٢ سم
4

ما قيمة ٤/∛٢ بعد إنطاق المقام؟

  • 1 ٢∛٤
  • 2 ٤∛٢
  • 3 ∛٤
  • 4 ٢∛٢
5

ما قيمة ١٠/√٥ بعد إنطاق المقام؟

  • 1 ٢√٥
  • 2 ٥√٢
  • 3 ١٠√٥
  • 4 √٥
6

ما قيمة ٦/√٣ بعد إنطاق المقام؟

  • 1 ٢√٣
  • 2 ٣√٢
  • 3 ٦√٣
  • 4 √٣

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