Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers InText Questions

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers InText Questions

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers InText Questions

Recap Exercise (Text Book Page No. 3)

Question 1.

Question 1.
Is the square of a prime number, prime?
Answer:
No, the square of a prime number ‘P’ has at Least 3 divisors 1, P and P². But a prime number is a number which has only two divisors, 1 and the number itself. So square of a prime number is not prime.

Question 2.
Will the sum of two perfect squares always be a perfect square? What about their difference and their product?
Answer:
The sum of two perfect squares, need not be always a perfect square. Also the difference of two perfect squares need not be always a perfect square. Bu the product of two perfect square is a perfect square.

Try These (Text Book Page No. 26)

Question 1.
Which among 256, 576, 960, 1025,4096 are perfect square numbers? (Hint: Try to extend the table of squares already seen).
Answer:
256 = 16²
576 = 24²
4096 = 64²
∴ 256, 576, and 4096 are perfect squares

 

Question 2.
One can judge just by look that each of the following numbers 82, 113, 1972, 2057, 8888, 24353 is not a perfect square. Explain why?
Answer:
Because the unit digit ola perfect square will be 0, 1,4, 5, 6, 9. But the given numbers have unit digits 2, 3, 7, 8. So they are not perfect squares.

Think (Text Book Page No. 27)

Consider the claim: “Between the squares of the consecutive numbers n and (n + 1), there are 2n non-square numbers’ Can it be true? FInd how many non-square numbers are there
(i) between 4 and 9 ?
(ii) between 49 and 64? and Verify the claim.
Answer:

Therefore we conclude that there are 2n non-square numbers between two consecutive square numbers.

Think (Text Book Page No. 30)

In this case, if we want to find the smallest factor with which we can multiply or divide 108 to get a square number, what should we do?
Answer:
108 = 2 × 2 × 3 × 3 = 2² × 3² × 3
If we multiply the factors by 2, then we get
2² × 3² × 3 × 3 = 2² × 3² × 3² = (2 × 3 × 3)²
Which is perfect square.
∴ Again if we divide by 3 then we get 2² × 3² ⇒ (2 × 3)², a perfect square.
∴ We have to multiply or divide 108 by 3 to get a perfect square.

 

Try These (Text Book Page No. 32)

Find the square root by long division method.
Question 1.
400
Answer:

√400 = 20

Question 2.
1764
Answer:

√1764 = 42

 

Question 3.
9801
Answer:

√9801 = 66

Try These (Text Book Page No. 32)

without calculating the square root, guess the number of digits in the square root of the following numbers:

Try These (Text Book Page No. 33)

Find the square root of
Question 1.
5.4756
Answer:

Question 2.
19.36
Answer:

 

Question 3.
116.64
Answer:

Think (Text Book Page No. 33)

Try to fill in the blanks using √ab = √a × √b

Answer:

 

Try These (Text Book Page No. 34)

Question 2.
7, √65, 8
Answer:
Squaring 7, √65 and 8 we get 7², (√65)², 8² ⇒ 49, 65, 64
Ascending order : 49, 64, 65
Ascending order: 7, 8, √65

 

Try These (Text Book Page No. 37)

Find the ones digit in the cubes of each of the following numbers.
(i) 12
(ii) 27
(iii) 38
(iv) 53
(v) 71
(vi) 84
Answer:
(i) 12
12 ends with 2, so its cube ends with 8 i.e. ones digit in 12³ is 8.

(ii) 27
27 ends with 7, so its cube end with 3. i.e., ones digit in 27³ is 3.

(iii) 38
38 ends with 8, so its cube ends with 2 i.e. ones digit in 38³ is 2.

(iv) 53
53 ends with 3, so its cube ends with 7. i.e, ones digit in 53³ is 7.

(v) 71
71 ends with 1, so its cube ends with 1. i.e. ones digit in 71³ is 1

(vi) 84
84 ends with 4, so its cube ends with 4. i.e, ones digit in 84³ is 4.

 

Try These (Text Book Page No. 41)

Expand the following numbers using exponents:
(i) 8120
(ii) 20,305
(iii) 3652.01
(iv) 9426.521
Answer:
(i) 8120
8120 = (8 × 1000) + (1 × 100) + (2 x×10) + 0 × 1
= (8 × 10³) + (1 × 10²) + (2 × 10¹)

(ii) 20,305
20305 = (2 × 10000) + (0 × 1000) + (3 × 100) + (0 × 10) + (5 × 1)
= (2 × 10⁴) + (3 × 10²) + 5

Try These (Text Book Page No. 44)

Question 1.
Write in standard form: Mass of planet Uranus is 8.68 × 10²⁵ kg.
Answer:
Mass of Planet Uranus = 86800000000000000000000000 kg
[23 zeros after 88]

Question 2.
Write in scientific notation:
(i) 0.000012005
Answer:
0.000012005 = 1.2005 × 10^-5

(ii) 43 12.345
Answer:
43 12.345 = 4.312345 × 10³

 

(iii) 0.10524
Answer:
0.10524 = 1.0524 × 10^-1

(iv) The distance between the Sun and the planet Saturn 1.4335 × 10¹² miles.

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