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
