Question

1. Find a Pythagorean triplet whose one member is 10.

2. Find the √19801 by prime factorization method.

3. Find the √63×28

4. Check whether 4096 is a perfect cube.

5. What is the smallest number by which 675 can be multiplied to make it a perfect cube?​

Answer 1

Answer:

1.10 , 24 & 26 is a Pythagorean triplet whose smallest number is 10

2.(i) 729=3×3×3×3×3×3= 3

2

×3

2

×3

2

729

=27

(ii) 400= 2

2

×2

2

×5

2

400

=20

(iii) 1764= 2

2

×2

2

×7

2

1764

=42

(iv) 4096= 2

2

×2

2

×2

2

×2

2

×2

2

×2

2

4096

=64

(v) 7744= 2

2

×2

2

×2

2

×11

2

7744

=88

(vi) 9604= 2

2

×7

2

×7

2

9604

=98

(vii) 5929= 11

2

×7

2

5929

=77

(viii) 9216= 96

2

9216

=96

(ix) 529=23×23

529

=23

(x) 8100=90

2

8100

=90.

3.Here we first calculate the square root of the numerator and the square root of the denominator separately, and then we divide the two:

√63

√28

≈

7.9373

5.2915

= 1.5

Alternatively, we first divide 63 by 28 and then do the square root of the quotient:

√63/28 = √2.25 = 1.5

4.The value of the cube root of 4096 is 16. It is the real solution of the equation x3 = 4096. The cube root of 4096 is expressed as ∛4096 in radical form and as (4096)⅓ or (4096)0.33 in the exponent form. As the cube root of 4096 is a whole number, 4096 is a perfect cube

5.The smallest number by which 675 must be multiplied to obtain a perfect cube is 5.