Surds
 Simplify; ^{3}/_{(√7 − 2)} + ^{1}/_{√7} leaving the answer in the form a + b c , where a, b and c are rational numbers
 Given that:
2+√5 − 3 + √5 = a+b√5
2√5 2+√5
Find the values of a and b where a and b are rational numbers  If:
14 − 14 = a√7 + b√2
7  √12 7 + √2
Find the values of a and b, where a and b are rational numbers *  Rationalize the denominator
2 − √2
(√2 − 1)^{3}and express your answer in the form of a + c√2  The figure below is a right pyramid with a rectangular base ABCD and vertex V.
O is the centre of the base and M is a point on OV such that OM = ^{1}/_{3 }OV, AB = 8 cm, BC = 6 cm and VA = VB=VD = VC = 15 cm. Find ; The height OV of the pyramid.
 The angle between the plane BMC and base ABCD.
 Find the value of y which satisfies the equation
Log _{10}5 – 2 + log_{10 }(2y + 10) = log_{10 }(y – 4)  Simplify the expression
√ 3  √2 giving your answer in the for of a + b√c.
√3 + √2
Answers




 (2 – 3 ) (3 + 2)
3(2)2 – 2)2
3x2 – 3 + 2 – 2
9x2 – 4x3
6 – 3 + 2 – 6
18 – 12 = 6  Or = 16^{2 } 5^{2}= √(256 – 25)
= 15.198 cm  tan θ=^{ 5.066}/_{4} = 1.2665
∴ θ51.710
 Or = 16^{2 } 5^{2}= √(256 – 25)
 Log_{10}5 – log_{10}10^{2 }+ log_{10}(2y + 10) = log_{10}(y – 4)
Log_{10}{^{5 (2y + 10)}/_{102}} = log _{10 }(y4)
10y + 50 = 100 y – 400
90 y = 450
y = 5 
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