Mr Daniels Maths
Surds:Brackets

Set 1

Set 2

Set 3

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

Q1) \( \sqrt { 3 } ( 2 + \sqrt { 5 } )= \) [ \(2\sqrt{3}\) + \(\sqrt{15}\) ]

Q1) \((1 + \sqrt2)(3+ \sqrt3 ) \) [ 3+\(\sqrt{3}\)+\(3\sqrt{2}\)+\(\sqrt{6}\)]

Q2) \(4 ( 3 + \sqrt { 5 } )= \) [ \(12 + \) \(4\sqrt{5}\)]

Q2) \( \sqrt { 3 } ( 4 + \sqrt { 7 } )= \) [ \(4\sqrt{3}\) + \(\sqrt{21}\) ]

Q2) \((3 + \sqrt2)(3+ \sqrt2 ) \) [ 11+\(6\sqrt{2}\)]

Q3) \(5 ( 5 + \sqrt { 6 } )= \) [ \(25 + \) \(5\sqrt{6}\)]

Q3) \( \sqrt { 4 } ( 2 + \sqrt { 8 } )= \) [ \(4\) + \(4\sqrt{2}\) ]

Q3) \((5 + \sqrt15)(5+ \sqrt21 ) \) [ 25+\(5\sqrt{21}\)+\(5\sqrt{15}\)+\(3\sqrt{35}\)]

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

Q4) \( \sqrt { 4 } ( 5 + \sqrt { 14 } )= \) [ \(10\) + \(2\sqrt{14}\) ]

Q4) \((1 + \sqrt2)(2+ \sqrt2 ) \) [ 4+\(3\sqrt{2}\)]

Q5) \(4 ( 5 + \sqrt { 15 } )= \) [ \(20 + \) \(4\sqrt{15}\)]

Q5) \( \sqrt { 3 } ( 5 + \sqrt { 2 } )= \) [ \(5\sqrt{3}\) + \(\sqrt{6}\) ]

Q5) \((2 + \sqrt2)(1+ \sqrt2 ) \) [ 4+\(3\sqrt{2}\)]

Q6) \(3 ( 5 + \sqrt { 6 } )= \) [ \(15 + \) \(3\sqrt{6}\)]

Q6) \( \sqrt { 3 } ( 3 + \sqrt { 5 } )= \) [ \(3\sqrt{3}\) + \(\sqrt{15}\) ]

Q6) \((5 + \sqrt5)(2+ \sqrt3 ) \) [ 10+\(5\sqrt{3}\)+\(2\sqrt{5}\)+\(\sqrt{15}\)]

Q7) \(5 ( 3 + \sqrt { 11 } )= \) [ \(15 + \) \(5\sqrt{11}\)]

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

Q7) \((1 + \sqrt2)(4+ \sqrt3 ) \) [ 4+\(\sqrt{3}\)+\(4\sqrt{2}\)+\(\sqrt{6}\)]

Q8) \(5 ( 1 + \sqrt { 3 } )= \) [ \(5 + \) \(5\sqrt{3}\)]

Q8) \( \sqrt { 2 } ( 3 + \sqrt { 2 } )= \) [ \(3\sqrt{2}\) + \(2\) ]

Q8) \((2 + \sqrt2)(3+ \sqrt3 ) \) [ 6+\(2\sqrt{3}\)+\(3\sqrt{2}\)+\(\sqrt{6}\)]

Q9) \(3 ( 3 + \sqrt { 8 } )= \) [ \(9 + \) \(6\sqrt{2}\)]

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

Q9) \((2 + \sqrt3)(4+ \sqrt6 ) \) [ 8+\(2\sqrt{6}\)+\(4\sqrt{3}\)+\(3\sqrt{2}\)]

Q10) \(2 ( 1 + \sqrt { 2 } )= \) [ \(2 + \) \(2\sqrt{2}\)]

Q10) \( \sqrt { 3 } ( 5 + \sqrt { 13 } )= \) [ \(5\sqrt{3}\) + \(\sqrt{39}\) ]

Q10) \((3 + \sqrt3)(1+ \sqrt3 ) \) [ 6+\(4\sqrt{3}\)]