Question

fill in the blanks the value of a is. ,b is and the square roots 361 IS 19​

Answer 1

SOLUTION

TO DETERMINE

To fill in the blanks :

(а) The perfect square number between 60 and 70 is ______

(b) The square root of 361 ends with digit ______

EVALUATION

ANSWER TO QUESTION : (a)

We have

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

Hence we can conclude that :

The perfect square number between 60 and 70 is 64

ANSWER TO QUESTION : (b)

Here the given number is 361

We now prime factorise the given number

361 = 19 × 19 = 19²

Thus we get

$\sf{ \sqrt{361} = \sqrt{ {19}^{2} } = 19 }$

Now unit digit of 19 = 9

Hence we can conclude that :

The square root of 361 ends with digit 9

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Answer 2

Complete Question :- fill in the blanks :-

(а) The perfect square number between 60 and 70 is ______ ?

(b) The square root of 361 ends with digit ______ ?

Solution :-

(a)

we know that, perfect square upto 100 are :-

→ 1² = 1

→ 2² = 4

→ 3² = 9

→ 4² = 16

→ 5² = 25

→ 6² = 36

→ 7² = 49

→ 8² = 64

→ 9² = 81

→ 10² = 100

as we can see that, 64 is the perfect square of number 8 that lies between 60 and 70 .

→ 60 < 64 < 70

therefore, the perfect square number between 60 and 70 is 64 .

(b) Basic Method :-

→ √(361)

→ √(19 * 19)

→ √(19)²

using √(a²) = a ,

→ 19

therefore, The square root of 361 ends with digit 9 .

Conceptual Method :-

concept for unit digit of a square number :-

→ 1² = 1 = unit digit 1 .

→ 2² = 4 = unit digit 4.

→ 3² = 9 = unit digit 9.

→ 4² = 16 = unit digit 6.

→ 5² = 25 = unit digit 5.

→ 6² = 36 = unit digit 6 .

→ 7² = 49 = unit digit 9.

→ 8² = 64 = unit digit 4.

→ 9² = 81 = unit digit 1.

→ 10² = 100 = unit digit 0.

So, unit digit of a square number is depends on the unit digit of square root of that number..

Conclusion :-

• unit digit 1 in last = 1 or 9.
• unit digit 4 in last = 2 or 8.
• unit digit 6 in last = 4 or 6.
• unit digit 9 in last = 3 or 7.
• unit digit 5 in last = 5
• unit digit 0 in last = 0 .

now, given number is 361

→ 361 = unit digit 1 in last = square root has 1 or 9 in last .

now,

→ 3(61) = Last two digits are to find unit digit of square root only .

now, as we can see that, left digit is 3 and upto 3 we can go to square of 1 as 1² = 1 .

then, we can conclude that, 361 is either square of 11 or 19 .

checking,

→ 11² = 11 * 11 = 121

→ 19² = 19 * 19 = 361

therefore, we can conclude that, square root of 361 is 19 .

Hence, The square root of 361 ends with digit 9 .

Note :- This method will help us in finding unit digit or square root of greater values .

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