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Show that 3+sqrt(5) is an irrational num...

Show that `3+sqrt(5)` is an irrational number, assuming that `sqrt(5)` is an irrational number.

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AGRAWAL PUBLICATION-SAMPLE PAPER 4-EXERCISE
  1. The figure shows the cross-section of the interior of thermos flask . ...

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  2. Without actually performing the long division, write the decimal expan...

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  3. Show that 3+sqrt(5) is an irrational number, assuming that sqrt(5) is ...

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  4. Solve algebraically: 4x + 3y = 14 and 3x - 4y = 23.

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  5. Evaluate: (sin^(4) 60^(@) + sec^(4) 30^(@)) - 2 (cos^(2) 45^(@) - sin^...

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  6. Prove that (sin theta - 2 sin^(3) theta)/(2 cos^(3) theta - cos theta)...

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  7. A die is thrown twice. Find the probability that: 5 will not come up...

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  8. Find a point on x - axis which is equidistant from A (-3, 4) and B(7, ...

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  9. If the circumference of a circle increases from 4pi to 8pi, then find ...

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  10. The sum of the squares of two consecutive multiples of 7 is 637. Find ...

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  11. The figure drawn on the graph paper shows a Delta ABC with vertices A ...

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  12. The figure drawn on the graph paper shows a Delta ABC with vertices A ...

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  13. The figure drawn on the graph paper shows a Delta ABC with vertices A ...

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  14. Prove that the length of the tangents drawn from an external point to ...

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  15. Two spotlights, P and Q are mounted on a vertical pole AB as shown. ...

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  16. The minute hand of a clock is 2 cm long. Find the area of the face of ...

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  17. Two spheres of same metal weight 1 Kg and 7 Kg. The radius of the smal...

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  18. A bag contains 15 white balls and some black balls. If the probability...

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  19. Two men on either sideof a 75 m high building and in line with base of...

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  20. In the given figure, PA, QB and RC each is perpendicular to AC such th...

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