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Simplify the following expressions:

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

(ii) (5 + \(\sqrt7\)) (5 - \(\sqrt7\))

(iii) (\(\sqrt8\) - \(\sqrt2\)) (\(\sqrt8\) - \(\sqrt2\))

(iv) (3 + \(\sqrt3\)) (3 - \(\sqrt3\))

(v)  (\(\sqrt5\) - \(\sqrt2\)) (\(\sqrt5\) - \(\sqrt2\))

1 Answer

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Best answer

(i) (11 + \(\sqrt11\))(11 - \(\sqrt11\)) = (11)2 - (\(\sqrt11\))2

Because (a + b)(a - b) = a2 - b2

= 121 - 11 = 110

(ii) (5 + \(\sqrt7\))(5 - \(\sqrt7\)) = (5)2 - (\(\sqrt7\))2

= 25 – 7 = 18

(iii) (\(\sqrt8\) - \(\sqrt2\))(\(\sqrt8\) + \(\sqrt2\)) = (\(\sqrt8\))2 - (\(\sqrt2\))2

= 8 – 2 = 6

(iv) (3 + \(\sqrt3\))(3 - \(\sqrt3\)) = (3)2 - (\(\sqrt3\))2

= 9 – 3 = 6

(v) (\(\sqrt5\) - \(\sqrt2\))(\(\sqrt5\) - \(\sqrt2\)) = (\(\sqrt5\))2 - (\(\sqrt2\))2

= 5 – 2 = 3

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