Can any expert solve this :

Can any expert solve this : VACATION ASSIGNMENT MATHEMATICS 1. Evaluate; a) d) e) 2. Findthecompound interest on 2" fortwo wears at mourn. 3. Calculate the amountand the compound mtereston annum For 2 ! Fars. a. Express 2 as a decimal correct to decimal places S. Eoress 4.3üas a vulgar fraction, 6. Insert three rational numbers between and . 7. Rationalize the denominator Of the following: i) a , the values of a and b. 8 -If a and bare rational numbers and 9. Express the following With a rational denominator: 10. Insert a rational number between %ßandv7. II. Prove that the foNowing {2 ii) 12. Insert two irrational numbers between 3 and 4. andq-.findthevalueof p2+q2and pi-qa 15. Find the compound intereston 20m , forl year at the rateof 16 annumcompo.unded quarterly. 16. A man invested 46875 at 4 % per annum compound for 3 years. Calculate : il the interest for the first year ii) the amount at the end of second year iiil the htetestfo«the third year.

Dear student,
Here is the solution of your asked query:

Q . 1 . a) {(64)}^{\frac{1}{3}} = {(4^{3})}^{\frac{1}{3}} = 4^{3 \times \frac{1}{3}} = 4 c) {(125)}^{\frac{- 1}{3}} = {(5^{3})}^{\frac{- 1}{3}} = 5^{3 \times \frac{- 1}{3}} = 5^{- 1} = \frac{1}{5} 8 . \frac{2 + \sqrt{3}}{2 - \sqrt{3}} = a + b \sqrt{3} \Rightarrow \frac{2 + \sqrt{3}}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} = a + b \sqrt{3} {rationalising the denominator} \Rightarrow \frac{{(2 + \sqrt{3})}^{2}}{2^{2} - {(\sqrt{3})}^{2}} = a + b \sqrt{3} \Rightarrow \frac{4 + 3 + 4 \sqrt{3}}{4 - 3} = a + b \sqrt{3} \Rightarrow 7 + 4 \sqrt{3} = a + b \sqrt{3} Comparing both sides we get; a = 7 and b = 4

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