9. Find the square root of the following numbers by the Prime Factorisation Method
and Division Method. (1)9801 (W) 4096
Answers
Answer:
Ncert solutions
Grade 8
Mathematics
Science
Chapters in NCERT Solutions - Mathematics , Class 8
Exercises in Squares and Square Roots
Question 4
Q4) Find the square roots of the following numbers by the Prime Factorization method:
(i) 729
(ii) 400
(iii) 1764
(iv) 4096
(v) 7744
(vi) 9604
(vii) 5929
(viii) 9216
(ix) 529
(x) 8100
Solution:
(i) 729
\sqrt{729}=\sqrt{3\times3\times3\times3\times3\times3}
729
=
3×3×3×3×3×3
= 3 x 3 x 3
= 27
(ii) 400
\sqrt{400}=\sqrt{2\times2\times2\times2\times5\times5}
400
=
2×2×2×2×5×5
= 2 x 2 x 5
= 20
(iii) 1764
\sqrt{1764}=\sqrt{2\times2\times3\times3\times7\times7}
1764
=
2×2×3×3×7×7
= 2 x 3 x 7
= 42
(iv) 4096
\sqrt{4096}=\sqrt{2\times2\times2\times2\times2\times2\times2\times2\times2\times2\times2\times2}=2\times2\times2\times2\times2\times2
4096
=
2×2×2×2×2×2×2×2×2×2×2×2
=2×2×2×2×2×2
= 64
(v) 7744
\sqrt{7744}=\sqrt{2\times2\times2\times2\times2\times2\times11\times11}
7744
=
2×2×2×2×2×2×11×11
= 2\times2\times2\times112×2×2×11
= 88
(vi) 9604
\sqrt{9604}=\sqrt{2\times2\times7\times7\times7\times7}
9604
=
2×2×7×7×7×7
= 2 x 7 x 7
= 98
(vii) 5929
\sqrt{5929}=\sqrt{7\times7\times11\times11}
5929
=
7×7×11×11
= 7 x 11
= 77
Answer: 1. 99
2. 64
Hope it help you