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Operations on Irrational Numbers

Add i 2√3-5√2...

Question

Add (i) $(2 \sqrt{3} - 5 \sqrt{2}) a n d (\sqrt{3} + 2 \sqrt{2})$

(ii) $(2 \sqrt{2} + 5 \sqrt{3} - 7 \sqrt{5}) a n d (3 \sqrt{3} - \sqrt{2} + \sqrt{5})$

(iii) $(\frac{2}{3} \sqrt{7} - \frac{1}{2} \sqrt{2} + 6 \sqrt{11}) a n d (\frac{1}{3} \sqrt{7} + \frac{3}{2} \sqrt{2} - \sqrt{11})$

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Solution

i)

(ii)

(iii)

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$(i) \frac{3}{7} + \frac{- 4}{9} - \frac{- 11}{7} - \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} - \frac{1}{3} - \frac{2}{5} (i i i) \frac{4}{7} - \frac{- 8}{9} - \frac{- 13}{7} + \frac{17}{9}$

Simplify :

(i) $\frac{3 \sqrt{2} - 2 \sqrt{3}}{3 \sqrt{2} + 2 \sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}$

(ii) $\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}}$

Q. Question 11
Find the values of a and b in each of the following

(i) \frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a - 6 \sqrt{3}

(i i) \frac{3 - \sqrt{5}}{3 + 2 \sqrt{5}} = a \sqrt{5} - \frac{19}{11}

(i i i) \frac{\sqrt{2} + \sqrt{3}}{3 \sqrt{2} - 2 \sqrt{3}} = 2 - b \sqrt{6}

(i v) \frac{7 + \sqrt{5}}{7 - \sqrt{5}} - \frac{7 - \sqrt{5}}{7 + \sqrt{5}} = a + \frac{7}{11} \sqrt{5} b

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Solve

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

(k) (l)

(m) (n)

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