Quadratic Surd

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

Click on each question to see answer & solution.

Question No: #11

Largest surd among : $ \sqrt{2}, \sqrt[3]{3}, \sqrt[4]{5}, \sqrt[6]{6} $ is -
(a) $ \sqrt[4]{5} $, (b) $ \sqrt[3]{3} $, (c) $ \sqrt[6]{6} $, (d) $ \sqrt{2} $
Ans: (a) $ \sqrt[4]{5} $
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Question No: #12

Write the following statements true or false.
(i) `(-3 - \sqrt{11})` is one of the rationalising factors of the surd `3 - \sqrt{11}`
(ii) `\sqrt{\pi}` is a quadratic surd.
(iii) All conjugate surds are rationalising factor.
(iv) `\sqrt{75}` and `\sqrt{147}` are like surds.
Ans: (i) True, (ii) False, (iii) True, (iv) True
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Question No: #13

If `x\sqrt{30} = \sqrt{35} \times \sqrt{42}`, then `x =` ...... ред

Question No: #14

Value of `6 \times `$\sqrt[3]{4}$ ` \times 3 \times `$\sqrt[3]{2}$ is ......

Question No: #15

If `x = \sqrt{7] + \sqrt{6}`, then the value of `(x + 1/x)` is ........
Ans: `2\sqrt{7}`
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Question No: #16

If `x = \sqrt{7+4\sqrt{3}}`, then the value of `(x - 1/x)` is .......
Ans: `2\sqrt{3}`
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Question No: #17

If `x = 5+2\sqrt{6}`, then find the value of `(\sqrt{x}+1/\sqrt{x})`.
Ans: `2\sqrt{3}`
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Question No: #18

(i) Show that `(7+\sqrt{2})` is a conjugate surd of mixed quadratic surd `(7-\sqrt{2})`,
(ii) Show that `-5 + \sqrt{2}` is not a conjugate surd of the mixed quadratic surd `5 + \sqrt{2}`.

Question No: #19

Conjugate surd of `\frac{1}{3 - 2\sqrt{2}}` is -
(a) `-3-2\sqrt{2}`, (b) `\frac{1}{3+2\sqrt{2}}`, (c) `3+2\sqrt{2}`, (d) `2\sqrt{2}-3`
Ans: (b) `\frac{1}{3+2\sqrt{2}}`
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Question No: #20

Which is larger between `(\sqrt{15}+\sqrt{3})` and `(\sqrt{10}+\sqrt{8})`?
Ans: `(\sqrt{10}+\sqrt{8})`
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