The document Extra Questions and Practice Exercise- Squares and Square Roots Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by VP Classes.

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**Question 1: **How many numbers lie between squares of:

(i) 27 and 28 (ii) 16 and 17 (iii) 97 and 98

Solution: We know that, between n^{2} and (n + 1)^{2}, there are 2n non-square numbers.

âˆ´ (i) Between 27 and 28, there are 2 * 27, i.e 54 numbers.

(ii) Between 16 and 17, there are 2 * 16, i.e. 32 numbers.

(iii) Between 97 and 98, there are 2 * 97, i.e. 194 numbers.

**Question 2: **Express 169 as the sum of first 13 odd numbers.

**Solution:** We have 169 = 13^{2}

= Sum of first 13 odd numbers

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25

= (1 + 25) + (3 + 23) + (5 + 21) + (7 + 19) + (9 + 17) + (11 + 15) + 13

= 26 + 26 + 26 + 26 + 26 + 26 + 13

= (6 * 26) + 13 = 156 + 13 = 169

**Question 3:** Write the Pythagorean triplet whose one member is 13.

**Solution:** When â€˜nâ€™ is a member of a Pythagorean triplet, then the triplet is

n^{2} â€“ 1, 2n, n^{2} + 1

or (13^{2} â€“ 1), (2 * 13), (13^{2} + 1)

or (169 â€“ 1), (26), (169 + 1)

or 168, 26 and 170

**Question 4: **Using prime factors, find the square root of 729.

**Solution:** We have

âˆ´ 729 = 3 * 3 * 3 * 3 * 3 * 3

= 3^{2} * 3^{2} * 3^{2}

âˆ´

**Question 5: **Find the smallest whole number by which 288 should be divided so as to get a perfect square. Also find the square root of the resulting number.

**Solution:** We have

288 = 2 * 2 * 2 * 2 * 2 * 3 * 3

= 2^{2} * 2^{2} * 2 * 3^{2}

= (2 * 2 * 3)^{2} * 2

â‡’

â‡’ 144 = (2 * 2 * 3)^{2}

â‡’ = 2 * 2 * 3 = 12

Thus, 288 is to be divided by 2 to get a perfect square.

i.e. The required smallest number = 2

Also

**Question 6:** Find the length of the side of a square whose area is 676 m^{2}.

**Solution: **

Now, let the side of the square = x m

âˆ´ Area = x^{2}

â‡’ x^{2} = 676

â‡’

â‡’ x= 26

âˆ´ The required side of the square = 26 m

**Question 7:** In a right triangle ABC, âˆ B = 90Â°. If AB = 12 cm, BC = 5 cm, then find AC.

**Solution:** We know that, in a right triangle, the side opposite to 90Â° is hypotenuse.

âˆ´ AC is the hypotenuse in DABC.

According to Phythagoras theorem,

(Hypotenuse)^{2} = [Sum of the squares of the other two sides]

âˆ´ AC^{2} = AB^{2} + BC^{2}

â‡’ AC^{2} = (12)^{2} + (5)^{2}

â‡’ AC^{2} = 144 + 25

â‡’ AC^{2} = 169 = (13)^{2}

â‡’

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