Quadratic Surd

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

Define conjugate surd. Give example. Write the conjugate surd of `\sqrt{a}-b`

Question No: #2

Subtracting `\sqrt{5}` from `\sqrt{125}` will yield -
(a) `\sqrt{80}`, (b) `\sqrt{120}`, (c) `100`, (d) None of these
Ans: (a) `\sqrt{80}`
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Question No: #3

If `p+q = \sqrt{13}` and `p - q = \sqrt{5}`, then value of `pq` is -
(a) 2, (b) 8, (c) 9, (d) 18
Ans: (a) 2
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Question No: #4

If `\sqrt{5}+\sqrt{4}=x`, then the value of `\sqrt{5}-\sqrt{4}` is -
(a) `2/x`, (b) `x/2`, (c) `1/x`, (d) `1`
Ans: (c) `1/x`
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Question No: #5

If `\sqrt{5}+\sqrt{3}=x`, then the value of `\sqrt{5}-\sqrt{3}` is -
(a) `1/x`, (b) `2/x`, (c) `x`, (d) `x/2`
Ans: (b) `2/x`
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Question No: #6

If `(\sqrt{3} - \sqrt{2})^x = (\sqrt{3} + \sqrt{2})`, then value of `x` is -
(a) `1`, (b) `2`, (c) `-2`, (d) `3`
Ans: (c) `-2`
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Question No: #7

If `(x - 1/x) = \sqrt{3}/2`, then value of `(x + 1/x)` is -
(a) `\sqrt{19}/2`, (b) `\sqrt{19}/4`, (c) `\sqrt{7}/2`, (d) None of these.
Ans: (a) `\sqrt{19}/2`
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Question No: #8

If one rationalising factor of `2\sqrt{6}` is `\sqrt{2x}`, then value of `x` is -
(a) 2, (b) 3, (c) 6, (d) `\sqrt{6}`
Ans: (b) 3
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Question No: #9

If `\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}`, then value of `a` is -
(a) `4`, (b) `-4`, (c) `1`, (d) `-2`
Ans: (b) `-4`
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Question No: #10

If `\sqrt{x+5} + \sqrt{5-x} = 4`, then `x` =? -
(a) `\pm 3`, (b) `\pm 4`, (c) `\pm 5`, (d) `2.6`
Ans: (b) `\pm 4`
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