Math Problem Statement

  1. 3(5√2) =
  2. (2√3)(√15) =
  3. 3(2√3-4√5) =
  4. √3(5√6+4√3) =
  5. (1+√2)(3+√2) =
  6. (√2+√12)(√18+3√3) =
  7. (√3-2√5)(√3-2√5) =
  8. (3-√5)(3+√5) =
  9. (2√3+√2)(2√3-√2)=
  10. (1³√8)(4+³√2)=

Solution

Let's solve these step by step:

  1. 3(52)3(5\sqrt{2}) 3×52=1523 \times 5\sqrt{2} = 15\sqrt{2}

  2. (23)(15)(2\sqrt{3})(\sqrt{15}) 23×15=23×15=245=2×35=652\sqrt{3} \times \sqrt{15} = 2\sqrt{3 \times 15} = 2\sqrt{45} = 2 \times 3\sqrt{5} = 6\sqrt{5}

  3. 3(23−45)3(2\sqrt{3} - 4\sqrt{5}) 3×23−3×45=63−1253 \times 2\sqrt{3} - 3 \times 4\sqrt{5} = 6\sqrt{3} - 12\sqrt{5}

  4. 3(56+43)\sqrt{3}(5\sqrt{6} + 4\sqrt{3}) 3×56+3×43=518+49=5×32+4×3=152+12\sqrt{3} \times 5\sqrt{6} + \sqrt{3} \times 4\sqrt{3} = 5\sqrt{18} + 4\sqrt{9} = 5 \times 3\sqrt{2} + 4 \times 3 = 15\sqrt{2} + 12

  5. (1+2)(3+2)(1 + \sqrt{2})(3 + \sqrt{2}) [ 1 \times 3 + 1 \times \sqrt{2} + \sqrt{2} \times

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Math Problem Analysis

Mathematical Concepts

Simplification of Radicals
Multiplication of Radicals
Binomial Expansion
Conjugates

Formulas

a√b * c√d = ac√(b*d)
(a + b)(c + d) = ac + ad + bc + bd
(a + b)(a - b) = a^2 - b^2

Theorems

Distributive Property
Difference of Squares

Suitable Grade Level

Grades 8-10

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