Mr Daniels Maths
Surds:Brackets

Set 1

Set 2

Set 3

Q1) \(5 ( 4 + \sqrt { 19 } )= \) [ \(20 + \) \(5\sqrt{19}\)]

Q1) \( \sqrt { 5 } ( 4 + \sqrt { 12 } )= \) [ \(4\sqrt{5}\) + \(2\sqrt{15}\) ]

Q1) \((5 + \sqrt15)(4+ \sqrt11 ) \) [ 20+\(5\sqrt{11}\)+\(4\sqrt{15}\)+\(\sqrt{165}\)]

Q2) \(4 ( 2 + \sqrt { 8 } )= \) [ \(8 + \) \(8\sqrt{2}\)]

Q2) \( \sqrt { 4 } ( 2 + \sqrt { 2 } )= \) [ \(4\) + \(2\sqrt{2}\) ]

Q2) \((5 + \sqrt5)(5+ \sqrt17 ) \) [ 25+\(5\sqrt{17}\)+\(5\sqrt{5}\)+\(\sqrt{85}\)]

Q3) \(2 ( 3 + \sqrt { 6 } )= \) [ \(6 + \) \(2\sqrt{6}\)]

Q3) \( \sqrt { 2 } ( 1 + \sqrt { 2 } )= \) [ \(\sqrt{2}\) + \(2\) ]

Q3) \((4 + \sqrt6)(2+ \sqrt3 ) \) [ 8+\(4\sqrt{3}\)+\(2\sqrt{6}\)+\(3\sqrt{2}\)]

Q4) \(2 ( 3 + \sqrt { 5 } )= \) [ \(6 + \) \(2\sqrt{5}\)]

Q4) \( \sqrt { 2 } ( 4 + \sqrt { 3 } )= \) [ \(4\sqrt{2}\) + \(\sqrt{6}\) ]

Q4) \((1 + \sqrt2)(1+ \sqrt2 ) \) [ 3+\(2\sqrt{2}\)]

Q5) \(3 ( 5 + \sqrt { 12 } )= \) [ \(15 + \) \(6\sqrt{3}\)]

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

Q5) \((3 + \sqrt7)(3+ \sqrt8 ) \) [ 9+\(6\sqrt{2}\)+\(3\sqrt{7}\)+\(2\sqrt{14}\)]

Q6) \(5 ( 1 + \sqrt { 2 } )= \) [ \(5 + \) \(5\sqrt{2}\)]

Q6) \( \sqrt { 4 } ( 1 + \sqrt { 3 } )= \) [ \(2\) + \(2\sqrt{3}\) ]

Q6) \((2 + \sqrt2)(1+ \sqrt2 ) \) [ 4+\(3\sqrt{2}\)]

Q7) \(3 ( 3 + \sqrt { 8 } )= \) [ \(9 + \) \(6\sqrt{2}\)]

Q7) \( \sqrt { 3 } ( 4 + \sqrt { 8 } )= \) [ \(4\sqrt{3}\) + \(2\sqrt{6}\) ]

Q7) \((1 + \sqrt2)(2+ \sqrt2 ) \) [ 4+\(3\sqrt{2}\)]

Q8) \(3 ( 4 + \sqrt { 7 } )= \) [ \(12 + \) \(3\sqrt{7}\)]

Q8) \( \sqrt { 4 } ( 1 + \sqrt { 2 } )= \) [ \(2\) + \(2\sqrt{2}\) ]

Q8) \((5 + \sqrt2)(1+ \sqrt5 ) \) [ 5+\(5\sqrt{5}\)+\(\sqrt{2}\)+\(\sqrt{10}\)]

Q9) \(5 ( 1 + \sqrt { 3 } )= \) [ \(5 + \) \(5\sqrt{3}\)]

Q9) \( \sqrt { 3 } ( 1 + \sqrt { 2 } )= \) [ \(\sqrt{3}\) + \(\sqrt{6}\) ]

Q9) \((5 + \sqrt3)(3+ \sqrt6 ) \) [ 15+\(5\sqrt{6}\)+\(3\sqrt{3}\)+\(3\sqrt{2}\)]

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

Q10) \( \sqrt { 5 } ( 1 + \sqrt { 5 } )= \) [ \(\sqrt{5}\) + \(5\) ]

Q10) \((4 + \sqrt10)(3+ \sqrt8 ) \) [ 12+\(8\sqrt{2}\)+\(3\sqrt{10}\)+\(4\sqrt{5}\)]