Mr Daniels Maths
Surds:Brackets

Set 1

Set 2

Set 3

Q1) \(3 ( 4 + \sqrt { 12 } )= \) [ \(12 + \) \(6\sqrt{3}\)]

Q1) \( \sqrt { 4 } ( 2 + \sqrt { 8 } )= \) [ \(4\) + \(4\sqrt{2}\) ]

Q1) \((1 + \sqrt2)(2+ \sqrt2 ) \) [ 4+\(3\sqrt{2}\)]

Q2) \(3 ( 1 + \sqrt { 2 } )= \) [ \(3 + \) \(3\sqrt{2}\)]

Q2) \( \sqrt { 5 } ( 5 + \sqrt { 17 } )= \) [ \(5\sqrt{5}\) + \(\sqrt{85}\) ]

Q2) \((3 + \sqrt2)(3+ \sqrt6 ) \) [ 9+\(3\sqrt{6}\)+\(3\sqrt{2}\)+\(2\sqrt{3}\)]

Q3) \(2 ( 2 + \sqrt { 2 } )= \) [ \(4 + \) \(2\sqrt{2}\)]

Q3) \( \sqrt { 3 } ( 1 + \sqrt { 3 } )= \) [ \(\sqrt{3}\) + \(3\) ]

Q3) \((1 + \sqrt2)(4+ \sqrt2 ) \) [ 6+\(5\sqrt{2}\)]

Q4) \(5 ( 2 + \sqrt { 2 } )= \) [ \(10 + \) \(5\sqrt{2}\)]

Q4) \( \sqrt { 4 } ( 4 + \sqrt { 15 } )= \) [ \(8\) + \(2\sqrt{15}\) ]

Q4) \((4 + \sqrt8)(2+ \sqrt6 ) \) [ 8+\(4\sqrt{6}\)+\(4\sqrt{2}\)+\(4\sqrt{3}\)]

Q5) \(3 ( 5 + \sqrt { 15 } )= \) [ \(15 + \) \(3\sqrt{15}\)]

Q5) \( \sqrt { 2 } ( 3 + \sqrt { 3 } )= \) [ \(3\sqrt{2}\) + \(\sqrt{6}\) ]

Q5) \((1 + \sqrt3)(5+ \sqrt3 ) \) [ 8+\(6\sqrt{3}\)]

Q6) \(3 ( 3 + \sqrt { 5 } )= \) [ \(9 + \) \(3\sqrt{5}\)]

Q6) \( \sqrt { 5 } ( 5 + \sqrt { 18 } )= \) [ \(5\sqrt{5}\) + \(3\sqrt{10}\) ]

Q6) \((2 + \sqrt10)(5+ \sqrt6 ) \) [ 10+\(2\sqrt{6}\)+\(5\sqrt{10}\)+\(2\sqrt{15}\)]

Q7) \(5 ( 5 + \sqrt { 23 } )= \) [ \(25 + \) \(5\sqrt{23}\)]

Q7) \( \sqrt { 4 } ( 4 + \sqrt { 11 } )= \) [ \(8\) + \(2\sqrt{11}\) ]

Q7) \((3 + \sqrt5)(3+ \sqrt8 ) \) [ 9+\(6\sqrt{2}\)+\(3\sqrt{5}\)+\(2\sqrt{10}\)]

Q8) \(5 ( 4 + \sqrt { 3 } )= \) [ \(20 + \) \(5\sqrt{3}\)]

Q8) \( \sqrt { 5 } ( 1 + \sqrt { 2 } )= \) [ \(\sqrt{5}\) + \(\sqrt{10}\) ]

Q8) \((1 + \sqrt2)(3+ \sqrt2 ) \) [ 5+\(4\sqrt{2}\)]

Q9) \(2 ( 1 + \sqrt { 2 } )= \) [ \(2 + \) \(2\sqrt{2}\)]

Q9) \( \sqrt { 4 } ( 5 + \sqrt { 3 } )= \) [ \(10\) + \(2\sqrt{3}\) ]

Q9) \((3 + \sqrt14)(5+ \sqrt13 ) \) [ 15+\(3\sqrt{13}\)+\(5\sqrt{14}\)+\(\sqrt{182}\)]

Q10) \(5 ( 5 + \sqrt { 21 } )= \) [ \(25 + \) \(5\sqrt{21}\)]

Q10) \( \sqrt { 4 } ( 2 + \sqrt { 5 } )= \) [ \(4\) + \(2\sqrt{5}\) ]

Q10) \((2 + \sqrt6)(3+ \sqrt3 ) \) [ 6+\(2\sqrt{3}\)+\(3\sqrt{6}\)+\(3\sqrt{2}\)]