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**Q.1. Write four rational numbers equivalent to 5/7.****Ans. **We have,

â–º Four rational numbers equivalent to 5/7 are 10/14, 15/21, 20/28, 25/35.**Q.2. Find nine rational numbers between 0.1 and 0.2.****Ans. **Let x = 0.1, y = 0.2 and n = 9.__The nine rational numbers between x and y are:__

(x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d), (x + 6d), (x + 7d), (x + 8d) and (x + 9d).__Nine rational numbers between 0.1 and 0.2 are:__

(0.1 + 0.01); (0.1 + 0.02); (0.1 + 0.03); (0.1 + 0.04); (0.1 + 0.05); (0.1 + 0.06); (0.1 + 0.07); (0.1 + 0.08) and (0.1 + 0.09)

â–º 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18 and 0.19.**Q.3. Represent âˆš2 on the number line (or on the real line).****Ans. **

- Draw XOX' and mark O as 0.
- Take OA = 1 unit.
- Draw AB âŠ¥ OX and cut off AB = 1 unit.
- Now, OAB is a right triangle.

âˆµ OA^{2}+ AB^{2}= OB^{2}

â–º 1^{2}+ 1^{2}= OB^{2}

â–º 2 = OB^{2}

â–º OB =âˆš2 - With centre O and OB as radius, draw an arc intersecting OX at C.
- Thus, OC = âˆš2 on the real line XOX'.

**Q.4. Represent âˆš3 on the real line.****Ans. **

- Draw XOX ' and mark O as 0 on it.
- Take OA = 1 unit.
- Draw AB âŠ¥ OX and cut off AB = 1 unit.
- Join OB such that OAB is a right triangle.

âˆµ OA^{2}+ AB^{2}= OB^{2}

â–º 1^{2}+ 1^{2}= OB^{2}

â–º OB =âˆš2 - Again, draw BC âŠ¥ OB and cut off BC = 1 unit. Join OC.
- Now, OBC is a right triangle.

âˆµ OB^{2}+ BC^{2}= OC^{2}

â–º âˆš2^{2}+ 1^{2}= OC^{2}

â–º 2 + 1 = OB^{2}

â–º OC =âˆš3 - With centre as O and radius as OC draw an arc to intersect OX at D.
- Thus, OD =âˆš3 on the real line XOX'.

**Q.5. Express as a rational number in simplest form.****Ans.**

â–º 100x = 100 x (0.3838â€¦)

â–º 100x = 38.3838...(2)

Subtracting (1) from (2),

We have, 100x â€“ x = (38.3838â€¦) â€“ (0.3838â€¦)

**Q.6. Express in the form of .****Ans.**

âˆ´ 10x = 10 x (0.5353â€¦)

or 10x = 5.333... ...(1)

Also, 100x = 53.333... ...(2)

Subtracting (1) from (2),

â–º 100x â€“ 10x = (53.333â€¦) â€“ (5.333â€¦)

â–º 90x = 48**Q.7. Express is the form of p/q in the simplest form.****Ans.**

âˆ´ 1000x = 1000 x (0.003003â€¦)

or 1000x = 3.003003... â€¦(2)

Subtracting (1) from (2),

We have 1000x â€“ x = (3.003003â€¦) â€“ (0.003003â€¦)

â–º 999x = 3

â–º x = 3/999 = 1/333

Thus,**Q.8. Find the sum of (3âˆš3 +7âˆš2) and (âˆš3 - 5âˆš2)****Ans. **We have (3âˆš3 +7âˆš2) + (âˆš3 - 5âˆš2)

= âˆš3 3+7âˆš2 + âˆš3 - 5âˆš2

= (3âˆš3+âˆš3) + 7âˆš2 - 5âˆš2)

= âˆš3(3+1) + âˆš2(7-2)

= âˆš3(4) + âˆš2(5) = (4âˆš3 + 2âˆš2)**Q.9. Divide 15 âˆš12 by 3âˆš3.****Ans.****Q.10. If â€˜aâ€™ and â€˜bâ€™ are rational numbers and ****find the values of â€˜aâ€™ and â€˜bâ€™.****Ans.**

Comparing **Q.11. Find the value of when ****Ans.**

âˆµ

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