Summer Vacation Homework (Grade X Maths)

 


Q1. Rationalise the denominator:

  1. 1/√2
  2. 3/√5
  3. 5/2√3
  4. 7/√7
  5. 4/√11
  6. 6/3√2
  7. 2/(√3 + √2)
  8. 5/(√7 − √3)
  9. 3/(2 + √5)
  10. 4/(3 − √2)

Q2. Convert into rational form / Simplify:

  1. √18 / √2
  2. √50 / √2
  3. 3√12 / √3
  4. √45 / √5
  5. 2√75 / √3
  6. √98 / √2
  7. 4√27 / √3
  8. √32 / √2
  9. √72 / √2
  10. 5√48 / √3

Q3. Simplify using laws of exponents:

  1. 2³ × 2⁵
  2. 5⁶ ÷ 5²
  3. (3²)⁴
  4. 10⁴ × 10³
  5. 7⁵ ÷ 7³
  6. (2³)²
  7. 4³ × 4²
  8. 9⁵ ÷ 9²
  9. (5²)³
  10. 6⁴ ÷ 6²

Q4. Solve:

  1. (2⁵ × 2³) ÷ 2⁴
  2. 5⁷ ÷ (5² × 5³)
  3. (3⁶ × 3²) ÷ 3⁵
  4. (2⁴ × 2³) ÷ 2⁵
  5. 10⁶ ÷ 10²
  6. (7³ × 7²) ÷ 7⁴
  7. (4⁵ ÷ 4²) × 4³
  8. (9⁶ ÷ 9³) × 9²

Q5. Find the value:

  1. 2⁵
  2. 10⁶
  3. 3⁴ × 3²
  4. 5⁵
  5. 7⁴

Q6. Rationalise:

  1. 1/(√5 + √2)
  2. 4/(3 + √7)
  3. 6/(√3 − √2)
  4. 5/(√6 + √5)
  5. 2/(√8 − √3)

Q7. Word Problems:

  1. A number is written as 2⁶. Find its value.
  2. Find the value of 10⁵.
  3. Simplify 4³ × 4².
  4. If 3³ = 27, then find 3⁵.
  5. Rationalise 1/√8.

Activity Work:

  1. Write all laws of exponents with examples.
  2. Make a chart on rationalising denominator.
  3. Solve 10 extra sums on exponents.
  4. Learn squares from 1 to 30 and cubes from 1 to 15.

Happy Summer Vacation! 📚✏️