RBSE Class 8 Maths Important Questions Chapter 6 Square and Square Roots

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 6 Square and Square Roots Important Questions and Answers.

RBSE Class 8 Maths Chapter 6 Important Questions Square and Square Roots

Multiple Choice Questions:

Question 1.
Which of the following is not a perfect square number
(a) 2025
(b) 441
(c) 7928
(d) 6889
Answer:
(c) 7928

Question 2.
Which of the following numbers, whose square will have 1 at unit's place
(a) 109
(b) 82
(c) 77
(d) 123
Answer:
(a) 109

Question 3.
How many numbers in between 252 and 262 are not squares
(a) 25
(b) 26
(c) 51
(d) 50
Answer:
(d) 50

Question 4.
The least number by which 48 should be multiplied so get a number which is a perfect square—
(a) 2
(b) 3
(c) 4
(d) 12
Answer:
(b) 3

Question 5.
The square root of 6400 is
(a) 800
(b) 80
(c) 8
(d) none of the above
Answer:
(b) 80

Question 6.
The number of digits in the square root of 14400 is
(a) 3
(b) 4
(c) 5
(d) 2
Answer:
(a) 3

Question 7.
Which number will be odd in the given following numbers
(a) 16
(b) 19
(c) 22
(d) 24
Answer:
(b) 19

Question 8.
Which of the following numbers is not a perfect square number
(a) 49
(b) 72
(c) 81
(d) 225
Answer:
(b) 72

Fill in the blanks:

Question 1.
There can be only _____________ number of zeroes at the end of a perfect square number.
Answer:
even

Question 2.
There are _____________ numbers in between n² and (n + 1)².
Answer:
2n

Question 3.
21² - 20² = _____________
Answer:
41

Question 4.
Square root is the _____________ operation of square.
Answer:
inverse

Question 5.
To find the number of digits in the square root of a perfect square number, we use _____________
Answer:
bar.

Very Short Answer Type Questions:

Question 1.
Which all digits can come at the unit's place of perfect square?
Answer:
All perfect square have either 0, 1,4, 5, 6 or 9 at the unit's place.

Question 2.
If a number is having 3 zeroes at the end, how many zeroes will have it's square at the end?
Answer:
6 zeroes.

Question 3.
Find the sum without adding 1 + 3 + 5 + 7 + 9 + 11
Answer:
6² = 6 × 6 = 36

Question 4.
How many numbers are there in between 62 and 72?
Answer:
There are 2n numbers in between n² and (n + 1)².
Here n = 6,
Hence 2n = 2 × 6 = 12 numbers.

Question 5.
Find the product of 2 consecutive odd natural number 29 and 31.
Answer:
29 × 31 = (30 - 1) × (30 + 1)
= 30² - 1²
= 900 - 1
= 899

Question 6.
Find the square of 42.
Answer:
42² = (40 + 2)²
= 40(40 + 2) + 2(40 + 2)
= 40² + 40 × 2 + 2 × 40 + 2²
= 1600 + 80 + 80 + 4 = 1764

Question 7.
Find a set of Pythagorean triples if one of the numbers is 12.
Answer:
Let 2m = 12, so m = 6
Then m² - 1 = 6² - 1 = 36 - 1 = 35
and m² + 1 = 6² + 1 = 36 + 1 = 37
Hence the required triples are 12, 35, 37

Question 8.
Find the square root of 441 using factorization method.
Answer:

Question 9.
Find the square root of 6.25.
Answer:

∴ \(\sqrt{6.25}\) = 2.5

Short Answer Type Questions:

Question 1.
Find the smallest square number that is divisible by each of the numbers 6, 9 and 15.
Answer:
We know that LCM is the smallest number divisible by all its factors.
Since LCM of 6,9and 15 = 2 × 3 × 3 × 5 = 90
Now 90 = 2 × 3 × 3 × 5

Here the number 2, 5 are unpaired
∵ [90] × 2 × 5 = 2 × 3 × 3 × 5 × 2 × 5
or 900 = 2 × 2 × 3 × 3 × 5 × 5

∵ The prime factor of 900 are paired
∴ 900 is a perfect square
Thus the required number = 900

Question 2.
Find the smallest number which when divides 9408 gives the quotient as perfect square. Also find the square root of the quotient.
Answer:
By Prime factorisation 
9408 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 3
Since the prime factor 3 cannot be paired

∴ The given number should be divided by 3
\(\frac{9408}{3}=\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 3}{3}\)
= 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7
= 3136

which is a perfect square 2 588
and 2 294
\(\sqrt{3136}\) = 2 × 2 × 2 × 2 × 2 × 2 × 7 ×7
= 2 × 2 × 2 × 7
= 56