Problem 1 :
Simplify :
√3(√3 + √12)
Problem 2 :
Simplify :
-√2(-4 -√2)
Problem 3 :
Simplify :
√2(7 + √5 )
Problem 4 :
Simplify :
2(√4 + √10)
Problem 5 :
Simplify :
√5(√8 + √10)
Problem 6 :
Simplify :
√3(√9 + √21)
Problem 7 :
Simplify :
2√5(√6 + 2)
Problem 8 :
Simplify :
√14(3 - √4)
Problem 9 :
Simplify :
√21(5 + √7)
Problem 10 :
Simplify :
(5 - √3)(5 + √3)
Problem 1 :
Simplify :
√3(√3 + √12)
Solution :
√3(√3 + √12) = √3 ⋅ √3 + √3 ⋅ √12
√3(√3 + √12) = 3 + √(3 ⋅ 12)
√3(√3 + √12) = 3 + √36
√3(√3 + √12) = 3 + 6
√3(√3 + √12) = 9
Problem 2 :
Simplify :
-√2(-4 -√2)
Solution :
-√2(-4 -√2) = (-√2) ⋅ (-4) + (-√2) ⋅ (-√2)
-√2(-4 -√2) = 4√2 + 2
Problem 3 :
Simplify :
√2(7 + √5 )
Solution :
√2(7 + √5 ) = √2 ⋅ 7 + √2 ⋅ √5
√2(7 + √5 ) = 7√2 + √(2 ⋅ 5)
√2(7 + √5 ) = 7√2 + √10
Problem 4 :
Simplify :
2(√4 + √10)
Solution :
2(√4 + √10) = 2 ⋅ √4 + 2 ⋅ √10
2(√4 + √10) = 2 ⋅ 2 + 2 ⋅ √10
2(√4 + √10) = 4 + 2√10
Problem 5 :
Simplify :
√5(√8 + √10)
Solution :
√5(√8 + √10) = √5 ⋅ √8 + √5 ⋅ √10
√5(√8 + √10) = √(5 ⋅ 8) + √(5 ⋅ 10)
√5(√8 + √10) = √40 + √50
√5(√8 + √10) = √(4 ⋅ 10) + √(25 ⋅ 2)
√5(√8 + √10) = 2√10 + 5√2
Problem 6 :
Simplify :
√3(√9 + √21)
Solution :
√3(√9 + √21) = √3 ⋅ √9 + √3 ⋅ √21
√3(√9 + √21) = √3 ⋅ 3 + √3 ⋅ √21
√3(√9 + √21) = 3√3 + √(3 ⋅ 21)
√3(√9 + √21) = 3√3 + √63
√3(√9 + √21) = 3√3 + √(9 ⋅ 7)
√3(√9 + √21) = 3√3 + 3√7
Problem 7 :
Simplify :
2√5(√6 + 2)
Solution :
2√5(√6 + 2) = 2√5 ⋅ √6 + 2√5 ⋅ 2
2√5(√6 + 2) = 2√(5 ⋅ 6) + 4√5
2√5(√6 + 2) = 2√30 + 4√5
2√5(√6 + 2) = 2√30 + 4√5
Problem 8 :
Simplify :
√14(3 - √4)
Solution :
√14(3 - √4) = √14 ⋅ 3 - √14 ⋅ √4
√14(3 - √4) = 3√14 - √14 ⋅ 2
√14(3 - √4) = 3√14 - 2√14
√14(3 - √4) = √14
Problem 9 :
Simplify :
√21(5 + √7)
Solution :
√21(5 + √7) = √21 ⋅ 5 + √21 ⋅ √7
√21(5 + √7) = 5√21 + √(21 ⋅ 7)
√21(5 + √7) = 5√21 + √147
√21(5 + √7) = 5√21 + √(49 ⋅ 3)
√21(5 + √7) = 5√21 + 7√3
Problem 10 :
Simplify :
(5 - √3)(5 + √3)
Solution :
Using the algebraic identity a2 - b2 = (a + b)(a - b),
(5 - √3)(5 + √3) = 52 - (√3)2
(5 - √3)(5 + √3) = 25 - 3
(5 - √3)(5 + √3) = 22
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