Quadratic Surd

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

Click on each question to see answer & solution.

Question No: #11

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: #12

(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: #13

Prove that, `(\sqrt{7} - \sqrt{3}) \lt (\sqrt{5} - 1)`.

Question No: #14

If `x = \sqrt{3} + \sqrt{2}`, then show that, `x^2 + 1/x^2 = 10`.

Question No: #15

If `2x = \sqrt{5}+1`, then show that, `x^2-x-1=0`

Question No: #16

If `x + 1/x = \sqrt{3}`, then find the value of `x^54 + x^42 + x^36 + x^12 + x^6 - 1`
Ans: `-2`
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Question No: #17

Find the simplest value of:
(i) `\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}`
(ii) `\frac{4\sqrt{3}}{2-\sqrt{2}} - \frac{30}{4\sqrt{3}-\sqrt{18}} - \frac{\sqrt{18}}{3-2\sqrt{3}}`
(iii) `\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2 - 1}} + \frac{x-\sqrt{x^2 - 1}}{x+\sqrt{x^2-1}}`
(iv) `\frac{3\sqrt{7}}{\sqrt{2}+\sqrt{5}} - \frac{5\sqrt{5}}{\sqrt{2}+\sqrt{7}} + \frac{\sqrt{2}}{\sqrt{5}+\sqrt{7}}`
Ans: (i) `2/3`, (ii) `4\sqrt{6}`, (iii) `2(2x^2-1)`, (iv) `0`
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Question No: #18

If `x + \sqrt{x^2-9} = 9`, then find the value of `x - \sqrt{x^2-9}`

Question No: #19

If `x = 2 + \sqrt{3}` and `x+y=4`, then find the simplest value of `xy + 1/{xy}`

Question No: #20

If `x = \frac{\sqrt{3}+1}{\sqrt{3}-1}` and `y = \frac{\sqrt{3}-1}{\sqrt{3}+1}`, then show that, `\frac{x^2+y^2}{x^2-y^2} = \frac{7\sqrt{3}}{12}`.