[Mathematics I] Numerical Processes (1) Surd (Solutions)

[Mr. Babatunde]

SOLUTION TO MATH 1 SURD TEST

10] Simplify the following (2√3 - 4)(2√3 + 4)

   = (2√3)^2 - 4^2 (Symbol ^ means Raise to Power)
   = 12 - 16
   ANS = -4

9] Simplify the following (5 + 3√2)(5 - 3√2)

   = 5^2 - (3√2)^2
   = 25 - 18
   ANS = 7

8] Simplify the following 2 / 3√5 + 4

   = (2 / 3√5 + 4) X (3√5 - 4 / 3√5 - 4) ie [ / means all over]
   = 2(3√5 - 4) / (3√5 + 4)(3√5 - 4)
   = 6√5 - 8 / (3√5)^2 - 4^2
   = 6√5 - 8 / 45 - 16
   ANS = 6√5 - 8 / 29

7] Given that √3 = 1.732, Evaluate 2/√3 to 2 d.p

   = 2/√3 X √3/√3
   = 2√3 / V3 x √3
   = 2√3 / 3 (√3 Is given to be 1.732)
   = 2 x 1.732 / 3
   ANS = 1.15

6] Without using table or Calculator, Evaluate
   √2/3(√0.54 + √6)

   = (√2/3 x √0.54) + (√2/3 x √6)
   = (√2x0.54/√3) + (√2x6/3) ie They are all inside square root each
   = (√0.36) + (√4)
   = 0.6 + 2
   ANS = 2.6

5] Simplify 2√3+2 / 2√3-2
            
   = (2√3+2 / 2√3-2) X (2√3+2 / 2√3+2)
   =  |___________________|

   = (2√3+2)(2√3+2) / (2√3-2)(2√3+2)

   = 12+4√3 + 4√3+4 / (2√3)^2 - 2^2

   = 16+8√3 / 12-4
   = 8(2 + √3) / 8
   ANS = 2 + √3

4] Rationalize the denominator of the following
   5/√5
   = 5/√5 x √5/√5
   = 5√5/5
   ANS = √5

3] Express the following to square root
   2√2
   = √4 x √2
   = √4x2
   ANS = √8

2] Express the following to square root
   5√5
   = √25 x √5
   = √25x5
   ANS = √125

1] Express the following to square root
   6√3
   = √36 x √3
   = √36x3
   ANS = √108

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