Question

question 1 =square root by prime factorisation
8100
529
1764
4096
7744
9604
5929
9216
questipn 2=is 90 is a perfect square ​

Answer 1

Answer:

 (i) 729                        The prime factorization of 729 is    

729=3×3×3×3×3×3

. By pairing the prime factors, we get

729=3×3−−−−×3×3−−−−×3×3−−−−

               

3 729

3 243

3 81

3 27

3 9

3

                 So,

729−−−√=3×3×3=27

(ii) 400 The prime factorisation of 400 is

400=2×2×2×2×5×5

. By the prime factors, we get

400=2×2−−−−×2×2−−−−×5×5−−−−

.

2 400

2 200

2 100

2 50

5 25

5

Therefore,

400−−−√=2×2×5=20

. (iii) 1764 The prime factorization of 1764 is

1764=2×2×3 ×3×7×7

. By pairing the prime factors, we get                

2 1764

2 882

3 441

3 147

7 49

7

1764=2×2−−−−×3 ×3−−−−−×7×7−−−−

               So,

1764−−−−√=2×3×7=42

.                 (iv) 4096 The prime factorization of 4096 is

4096=2×2×2×2×

2×2×2×2×2×2×2×2

.                 By pairing the prime factors, we get                

2 4096

2 2048

2 1024

2 512

2 256

2 128

2 64

2 32

2 16

2 8

2 4

2

4096=2×2−−−−×2×2−−−−×2×2−−−−×2×2−−−−×2×2−−−−×2×2−−−−

So,

4096−−−−√=2×2×2×2×2×2=64

(v) 7744 The prime factorization of 7744 is

7744=2×2×2×2×2×2×11×11

. By pairing the prime factors, we get                

2 7744

2 3872

2 1936

2 968

2 484

2 242

11 121

11

7744=2×2−−−−×2×2−−−−×2×2−−−−×11×11−−−−−−

So,

7144−−−−√=2×2×2×11=88

. (vi) 9604 The prime factorization of 9604 is

9604=2×2×7×7×7×7

By pairing the prime factors, we get                

2 9604

2 4802

7 2401

7 343

7 49

7

9604=2×2−−−−×7×7−−−−×7×7−−−−

So,

9604−−−−√=2×7×7=98

(vii) 5929 The prime factorization of 5929 is

5929=7×7×11×11

.                 By pairing the prime factors, we get                                

5929=7×7−−−−=11×11−−−−−−

So,

5929−−−−√=7×11=77

. (viii) 9216 The prime factorization of 9216 is

9216=2×2×2×2×2×2×2×2×2×2×3×3

By pairing the prime factors, we get

2 9216

2 4608

2 2304

2 1152

2 576

2 288

2 144

2 72

2 36

2 18

3 9

3

9216=2×2−−−−×2×2−−−−×2×2−−−−×2×2−−−−×2×2−−−−×3×3−−−−

So,

9216−−−−√=2×2×2×2×2×3=96

. (ix) 529 The prime factorization of 529 is

529=23×23

. By pairing the prime factors, we get

529=23×23−−−−−−

So,

529−−−√=23

(x) 8100 The prime factorization of 8100 is  

8100=2×2×3×3×3×3×5×5

. By pairing the prime factors, we get

2 8100

2 4050

3 2025

3 675

3 225

3 75

5 25

5

8100=2×2−−−−×3×3−−−−×3×3−−−−×5×5−−−−

So,

8100−−−−√=2×3×3×5=90