Is 2645 a perfect square find the smallest number by which it should be multiplied to make it a perfect square also find the square root?

2645 can be factorised as follows.

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For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620
For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620
Is the number 2645 a perfect square if not find the smallest number by which 2645 should be divided to get a square number also find the square root of it?
What must be added to 2645 to make it a perfect square?
How do you find smallest number by which is a perfect square?
Is 2601 a perfect square?

2645 = 5 x 23 x 23

Here, prime factor 5 does not have its pair.

If we divide this number by 5, then the number will become a perfect square.

Therefore, 2645 has to be divided by 5 to obtain a perfect square.

2645 ÷5 = 529 is a perfect square.

529 = 23 x 23

∴ `sqrt529` = 23

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620

Solution:

We have to find the smallest whole number by which the number should be divided so as to get a perfect square number

To get a perfect square, each factor of the given number must be paired.

(i) 252

Hence, prime factor 7 does not have its pair. If the number is divided by 7, then the rest of the prime factor will be in pairs. Therefore, 252 has to be divided by 7 to get a perfect square.

252 ÷ 7 = 36

36 is perfect square

36 = 2 × 2 × 3 × 3

= 22 × 32

= (2 × 3)2

Thus, √36 = 2 × 3 = 6

(ii) 2925

Hence, prime factor 13 does not have its pair. If the number is divided by 13, then the rest of the prime factor will be in pairs. Therefore, 2925 has to be divided by 13 to get a perfect square.

2925 ÷ 13 = 225

225 is a perfect square

225 = 5 × 5 × 3 × 3

= 52 × 32

= (5 × 3)2

Thus, √225 = 15

(iii) 396

Hence, prime factor 11 does not have its pair. If the number is divided by 11, then the rest of the prime factor will be in pairs.

Therefore, 396 has to be divided by 11 to get a perfect square.

396 ÷ 11 = 36

36 is a perfect square

36 = 3 × 3 × 2 × 2

= 32 × 22

= (3 × 2)2

Thus, √36 = 3 × 2 = 6

(iv) 2645

Hence, prime factor 5 does not have its pair. If the number is divided by 5, then the rest of the prime factor will be in pairs.

Therefore, 2645 has to be divided by 5 to get a perfect square.

2645 ÷ 5 = 529

529 is a perfect square

529 = 23 × 23

= 232

Thus, √529 = 23

(v) 2800

Hence, prime factor 7 does not have its pair. If the number is divided by 7, then the rest of the prime factor will be in pairs. Therefore, 2800 has to be divided by 7 to get a perfect square

2800 ÷ 7 = 400

400 is a perfect square

400 = 2 × 2 × 2 × 2 × 5 × 5

= 22 × 22 × 52

= (2 × 3 × 5)2

Thus, √400 = 2 × 2 × 5 = 20

(vi) 1620

Hence, prime factor 5 does not have its pair. If the number is divided by 5, then the rest of the prime factor will be in pairs.

Therefore, 1620 has to be divided by 5 to get a perfect square.

1620 ÷ 5 = 324

324 is a perfect square

324 = 2 × 2 × 3 × 3 × 3 × 3

= 22 × 32 × 32

= (2 × 3 × 3)2

Thus, √324 = 2 × 3 × 3 = 18

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

Video Solution:

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3 Question 6

Summary:

For each of the following numbers (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620, the smallest whole number by which it should be divided so as to get a perfect square and the square root of the square numbers are as follows (i) 7; √36 = 6 (ii) 13; √225 = 15 (iii) 11; √36 = 6 (iv) 5; √529 = 23 (v) 7; √400 = 20 and (vi) 5; √324 = 18

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Is the number 2645 a perfect square if not find the smallest number by which 2645 should be divided to get a square number also find the square root of it?

If the number is divided by 5, then the rest of the prime factor will be in pairs. Therefore, 2645 has to be divided by 5 to get a perfect square.

What must be added to 2645 to make it a perfect square?

Hence, the given number is not a perfect square. Thus, 2645 needs to be divided by 5 to become a perfect square. Thus, the required smallest whole number by which it should be divided so as to get a perfect square number is 5 and the square root is √529= 23.

How do you find smallest number by which is a perfect square?

L.C.M. of 8, 15 and 20 is 120. Here, prime factors 2, 3 and 5 have no pair. Therefore 120 must be multiplied by 2 x 3 x 5 to make it a perfect square. Hence, the smallest square number which is divisible by 8, 15 and 20 is 3600.

Is 2601 a perfect square?

The square root of 2601 is expressed as √2601 in the radical form and as (2601)^½ or (2601)^0.5 in the exponent form. The square root of 2601 is 51. It is the positive solution of the equation x² = 2601. The number 2601 is a perfect square.