## Surds

1. Simplify; 3/(√7 − 2) + 1/√7  leaving the answer in the form a + b c , where a, b and c are rational numbers
2. 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
3.  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 *
4. Rationalize the denominator
2 − √2
(√2 − 1)3
and express your answer in the form of a + c√2
5. 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 ;
1. The height OV of the pyramid.
2. The angle between the plane BMC and base ABCD.
6. Find the value of y which satisfies the equation
Log 105 – 2 + log10 (2y + 10) = log10 (y – 4)
7. Simplify the expression
√ 3 - √2 giving your answer in the for of a + b√c.
√3 + √2

1. 2. 3. 4. 5. (2 – 3 ) (3 + 2)
3(2)2 – 2)2
3x2 – 3 + 2 – 2
9x2 – 4x3
6 – 3 + 2 – 6
18 – 12 = 6
1. Or = 162 - 52
= √(256 – 25)
= 15.198 cm
2. tan θ= 5.066/4 = 1.2665
∴ θ51.710
6. Log105 – log10102 + log10(2y + 10) = log10(y – 4)
Log10{5 (2y + 10)/102} = log 10 (y-4)
10y + 50 = 100 y – 400
90 y = 450
y = 5
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Read 11651 times Last modified on Wednesday, 10 February 2021 07:01
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