Simplify the following expressions - i 11 - -1111 - -11 ii 5 - -75 - -7 iii -8 - -2-8 - -2 iv 3 - -33 - -3 v -5 - -2-5 - -2

(i) (11+ √(11))(11 √(11)) =(11)^2 (√(11))^2 {∵ (a+b)(a b)=a^2 b^2} =121 11 = 110 (ii) (5 + √(7))(5 √(7)) =(5)^2 (√(7))^2 {∵ (a+b)(a b)= ...

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Byju's Answer

Standard IX

Mathematics

Rationalisation

Simplify the ...

Question

Simplify the following expressions :

(i) $(11 + \sqrt{11}) (11 - \sqrt{11})$

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

(iii) $(\sqrt{8} - \sqrt{2}) (\sqrt{8} + \sqrt{2})$

(iv) $(3 + \sqrt{3}) (3 - \sqrt{3})$

(v) $(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})$

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Solution

(i) $(11 + \sqrt{11}) (11 - \sqrt{11}) = (11)^{2} - (\sqrt{11})^{2} {∵ (a + b) (a - b) = a^{2} - b^{2}} = 121 - 11 = 110$

(ii) $(5 + \sqrt{7}) (5 - \sqrt{7}) = (5)^{2} - (\sqrt{7})^{2} {∵ (a + b) (a - b) = a^{2} - b^{2}} = 25 - 7 = 18$

(iii) $(\sqrt{8} - \sqrt{2}) (\sqrt{8} + \sqrt{2}) = (\sqrt{8})^{2} - (\sqrt{2})^{2} {∵ (a + b) (a - b) = a^{2} - b^{2}} = 8 - 2 = 6$

(iv) $(3 + \sqrt{3}) (3 - \sqrt{3}) = (3)^{2} - (\sqrt{3})^{2} {∵ (a + b) (a - b) = a^{2} - b^{2}} = 9 - 3 = 6$

(v) $(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2}) = (\sqrt{5})^{2} - (\sqrt{2})^{2} {∵ (a + b) (a - b) = a^{2} - b^{2}} = 5 - 2 = 3$

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Similar questions

Q. Simplify the following expressions:

(i)

(11 + \sqrt{11}) (11 - \sqrt{11})

(ii)

(5 + \sqrt{7}) (5 - \sqrt{7})

(iii)

(\sqrt{8} - \sqrt{2}) (\sqrt{8} + \sqrt{2})

(iv)

(3 + \sqrt{3}) (3 - \sqrt{3})

(v)

(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})

source $(i) \frac{8}{9} + \frac{- 11}{6} (i i) 3 + \frac{5}{- 7} (i i i) \frac{1}{- 12} a n d \frac{2}{- 15} (i v) \frac{- 8}{19} + \frac{- 4}{57} (v) \frac{7}{9} + \frac{3}{- 4} (v i) \frac{5}{26} + \frac{11}{- 39} (v i i) \frac{- 16}{9} + \frac{- 5}{12} (v i i i) \frac{- 13}{8} + \frac{5}{36} (i x) 0 + \frac{- 3}{5} (x) 1 + \frac{- 4}{5} (x i) \frac{- 5}{16} + \frac{7}{24}$

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Q. Use the number line and add the following integers:
(i) 9 + (−6)
(ii) (−3) + 7
(iii) 8 + (−8)
(iv) (−1) + (−3)
(v) (−4) + (−7)
(vi) (−2) + (−8)
(vii) 3 + (−2) + (−4)
(viii) (−1) + (−2) + (−3)
(ix) 5 + (−2) + (−6)

Q. Simplify the following expressions:

(i)

(4 + \sqrt{7}) (3 + \sqrt{2})

(ii)

(3 + \sqrt{3}) (5 - \sqrt{2})

(iii)

(\sqrt{5} - 2) (\sqrt{3} - \sqrt{5})

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Simplify the following expressions : (i) (11+√11)(11−√11) (ii) (5+√7)(5−√7) (iii) (√8−√2)(√8+√2) (iv) (3+√3)(3−√3) (v) (√5−√2)(√5+√2)

Simplify the following expressions :

(i) $(11 + \sqrt{11}) (11 - \sqrt{11})$

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

(iii) $(\sqrt{8} - \sqrt{2}) (\sqrt{8} + \sqrt{2})$

(iv) $(3 + \sqrt{3}) (3 - \sqrt{3})$

(v) $(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})$