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Practice each question, then open the answer or worked solution.
A perfect square number having n digits where n is even will have square root with
(a) n + 1 digit (b) n/2 digit (c) n/3 digit (d) (n + 1)/2 digit
Solution:-
(b) n/2 digit
If m is the cube root of n, then n is
(a) m3 (b) √m (c) m/3 (d) 3√m
Solution:-
(a) m3
Given in the question,
3√n = m
n = m3
The value of √(248 + √(52 + √144)) is
(a) 14 (b) 12 (c) 16 (d) 13
Solution:-
(c) 16
√(248 + √(52 + √144))
= √(248 + √(52 + 12))
= √(248 + √(64))
= √(248 + 8)
= √(256)
= 16
Given that √4096 = 64, the value of √4096 + √40.96 is
(a) 74 (b) 60.4 (c) 64.4 (d) 70.4
Solution:-
(d) 70.4
√4096 + √40.96
= 64 + 6.4
= 70.4
In questions 25 to 48, fill in the blanks to make the statements true.
There are _________ perfect squares between 1 and 100.
Solution:-
There are 8 perfect squares between 1 and 100.
2 × 2 = 4
3 × 3 = 9
4 × 4 = 16
5 × 5 = 25
6 × 6 = 36
7 × 7 = 49
8 × 8 = 64
9 × 9 = 81
There are _________ perfect cubes between 1 and 1000.
Solution:-
There are 8 perfect cubes between 1 and 1000.
2 × 2 × 2 = 8
3 × 3 × 3 = 27
4 × 4 × 4 = 64
5 × 5 × 5 = 125
6 × 6 × 6 = 216
7 × 7 × 7 = 343
8 × 8 × 8 = 512
9 × 9 × 9 = 729
The units digit in the square of 1294 is _________.
Solution:-
The units digit in the square of 1294 is 6.
We know that, 4 or 6 at the units place ends in 6.
The square of 500 will have _________ zeroes.
Solution:-
The square of 500 will have 4 zeroes.
5002 = 500 × 500 = 25000
There are _________ natural numbers between n2 and (n + 1)2.
Solution:-
There are 2n natural numbers between n2 and (n + 1)2.
The square root of 24025 will have _________ digits.
Solution:-
The square root of 24025 will have 3 digits.
The number given in the question has 5 digits,
i.e. n = 5
Then,
= (n + 1)/2
= (5 + 1)/2
= 6/2
= 3