Question

1. Find the square root of each of the following numbers by Prime Factorisation Method.

1) 729
2) 7744
3) 8100
4) 10404
5) 3136​

Answer 1

Step-by-step explanation:

$\huge\fbox\pink{A}\fbox\blue{n}\fbox\purple{S}\fbox\green{w}\fbox\red{E}\fbox\orange{r}$

$\\ {\large{\sf{\fbox{\orange{Finding square root by prime factorisation method \: - }}}}}$

${\bold{\sf{(i) \: \: 729}}}$

${\bold{\sf{\sqrt{729} \: = \: 3² × 3² × 3²}}}$

${\bold{\sf{→ \: 27}}}$

${\bold{\sf{(ii) \: 7744}}}$

${\bold{\sf{\sqrt{7744} \: = \: 2² × 2² × 2² ×11²}}}$

${\bold{\sf{→ \: 88}}}$

${\bold{\sf{(iii) \: 8100}}}$

${\bold{\sf{\sqrt{8100} = \: 90²}}}$

${\bold{\sf{→ \: 90}}}$

${\bold{\sf{(iv) \: 10404}}}$

${\bold{\sf{\sqrt{10404} \: = \: 2² × 3² × 17²}}}$

${\bold{\sf{→ \: 102}}}$

${\bold{\sf{(v) \: 3136}}}$

${\bold{\sf{\sqrt{3136} \: = \: 2² × 2² × 2² × 7²}}}$

${\bold{\sf{→ \: 56}}}$

$\\ {\large{\sf{\fbox{\red{Hope it's help}}}}}$

Answer 2

Step-by-step explanation:

(i)729

{\bold{\sf{\sqrt{729} \: = \: 3² × 3² × 3²}}}

729

=3²×3²×3²

{\bold{\sf{→ \: 27}}}→27

{\bold{\sf{(ii) \: 7744}}}(ii)7744

{\bold{\sf{\sqrt{7744} \: = \: 2² × 2² × 2² ×11²}}}

7744

=2²×2²×2²×11²

{\bold{\sf{→ \: 88}}}→88

{\bold{\sf{(iii) \: 8100}}}(iii)8100

{\bold{\sf{\sqrt{8100} = \: 90²}}}

8100

=90²

{\bold{\sf{→ \: 90}}}→90

{\bold{\sf{(iv) \: 10404}}}(iv)10404

{\bold{\sf{\sqrt{10404} \: = \: 2² × 3² × 17²}}}

10404

=2²×3²×17²

{\bold{\sf{→ \: 102}}}→102

{\bold{\sf{(v) \: 3136}}}(v)3136

{\bold{\sf{\sqrt{3136} \: = \: 2² × 2² × 2² × 7²}}}

3136

=2²×2²×2²×7²

{\bold{\sf{→ \: 56}}}→56

\begin{gathered} \\ {\large{\sf{\fbox{\red{Hope it's help}}}}}\end{gathered}