SEBA Class 10 Maths Revision 1 Solutions (2026–27)

Q1. What will be the digits in the unit place of the squares of the following numbers?
(i) 272    (ii) 79    (iii) 400    (iv) 2637
Answer:
To find the unit digit of a square, we only need to look at the unit digit of the number.

(i) 272 → unit digit = 2 → \(2^2 = 4\)
(ii) 79 → unit digit = 9 → \(9^2 = 81\) → unit digit = 1
(iii) 400 → unit digit = 0 → \(0^2 = 0\)
(iv) 2637 → unit digit = 7 → \(7^2 = 49\) → unit digit = 9

Final Answer:
(i) 4    (ii) 1    (iii) 0    (iv) 9

Q2. Why do the following numbers are not perfect square?
(i) 1057    (ii) 7982    (iii) 2221    (iv) 640
Answer:
A perfect square can only have certain digits at the unit place: 0, 1, 4, 5, 6, or 9.
If a number ends with 2, 3, 7, or 8, it cannot be a perfect square.

(i) 1057 → unit digit = 7 → not a perfect square
(ii) 7982 → unit digit = 2 → not a perfect square
(iii) 2221 → unit digit = 1 → possible, but not a perfect square (no integer square root)
(iv) 640 → unit digit = 0 → but not a perfect square (not exact square)

Final Conclusion:
These numbers are not perfect squares because they do not satisfy the properties of perfect squares.

Q3. What are the squares of the following numbers?
(i) 19    (ii) 37    (iii) 53    (iv) 78
Answer:
To find the square of a number, we multiply the number by itself.

(i) \(19^2 = 19 \times 19 = 361\)
(ii) \(37^2 = 37 \times 37 = 1369\)
(iii) \(53^2 = 53 \times 53 = 2809\)
(iv) \(78^2 = 78 \times 78 = 6084\)

Final Answer:
(i) 361    (ii) 1369    (iii) 2809    (iv) 6084

Q4. Find the square roots of the following numbers.
(i) 1764    (ii) 9216    (iii) 7744    (iv) 9801
Answer:
To find square roots, we check which number when multiplied by itself gives the given number.

(i) \(42^2 = 1764\) → √1764 = 42
(ii) \(96^2 = 9216\) → √9216 = 96
(iii) \(88^2 = 7744\) → √7744 = 88
(iv) \(99^2 = 9801\) → √9801 = 99

Final Answer:
(i) 42    (ii) 96    (iii) 88    (iv) 99

Q5. Find the least numbers (integer) with which the following numbers are to be multiplied so that they become perfect squares.
(i) 125    (ii) 1008    (iii) 2028    (iv) 768
Answer:
We find prime factors and make all powers even.

(i) \(125 = 5^3\) → multiply by 5 → \(5^4\)
Answer = 5

(ii) \(1008 = 2^4 \times 3^2 \times 7\) → multiply by 7
Answer = 7

(iii) \(2028 = 2^2 \times 3 \times 13^2\) → multiply by 3
Answer = 3

(iv) \(768 = 2^8 \times 3\) → multiply by 3
Answer = 3

Final Answer:
(i) 5    (ii) 7    (iii) 3    (iv) 3

Q6. With what least numbers (integer) the following numbers are to be divided so that they become perfect squares.
(i) 468    (ii) 1584    (iii) 2645    (iv) 1620
Answer:
We divide by factors whose powers are odd.

(i) \(468 = 2^2 \times 3^2 \times 13\) → divide by 13
Answer = 13

(ii) \(1584 = 2^4 \times 3^2 \times 11\) → divide by 11
Answer = 11

(iii) \(2645 = 5 \times 23^2\) → divide by 5
Answer = 5

(iv) \(1620 = 2^2 \times 3^4 \times 5\) → divide by 5
Answer = 5

Final Answer:
(i) 13    (ii) 11    (iii) 5    (iv) 5

Q7. Find the square root of the following decimal numbers.
(i) 12.25    (ii) 24.01    (iii) 146.41    (iv) 102.01
Answer:
Convert decimals into fractions or recognize known squares.

(i) \(3.5^2 = 12.25\) → √12.25 = 3.5
(ii) \(4.9^2 = 24.01\) → √24.01 = 4.9
(iii) \(12.1^2 = 146.41\) → √146.41 = 12.1
(iv) \(10.1^2 = 102.01\) → √102.01 = 10.1

Final Answer:
(i) 3.5    (ii) 4.9    (iii) 12.1    (iv) 10.1

Q8. Four options are given for each of the following. Find the correct option.

(a) Which of the following is a square of an odd natural number?

(a) 256
(b) 169
(c) 546
(d) 754

Answer: (b) 169

(b) Which of the following will have 1 (one) in the unit place?

(i) \(19^2\)
(ii) \(34^2\)
(iii) \(18^2\)
(iv) \(20^2\)

Answer: (i) \(19^2\)

(c) Between 18² and 19² how many natural numbers are there?

(a) 38
(b) 36
(c) 42
(d) 40

Answer: (b) 36

(d) Which of the following is not a perfect square?

(a) 441
(b) 572
(c) 576
(d) 729

Answer: (b) 572

(e) If \( \sqrt{2025} = 45 \), then \( \sqrt{20.25} \) is equal to

(a) 45
(b) 4.5
(c) 0.45
(d) 0.045

Answer: (b) 4.5