Question

$\sqrt{625}+\sqrt{441}=$

• A. $47$
• B. $\sqrt{1066}$
• C. $46$
• D. $45$

Answer 1

The correct option is C $46$

We are going to find square root by prime factorization method.

$625=5\times 125$

$\Rightarrow$ $625=5\times 5\times 25$

$\Rightarrow$ $625=5\times 5\times 5\times 5\times 5$

$\Rightarrow$ $625=5^4$

$\Rightarrow$ $\sqrt{625}=\sqrt{5^4}$

$\Rightarrow$ $\sqrt{625}=5^2$

$\Rightarrow$ $\sqrt{625}=25$ ----- ( 1 )

$441=3\times 147$

$\Rightarrow$ $441=3\times 3\times 49$

$\Rightarrow$ $441=3\times 3\times 7\times 7$

$\Rightarrow$ $441=3^2\times 7^2$

$\Rightarrow$ $\sqrt{441}=\sqrt{3^2\times 7^2}$

$\Rightarrow$ $\sqrt{441}=3\times 7$

$\Rightarrow$ $\sqrt{441}=21$ ----- ( 2 )

$\Rightarrow$ $\sqrt{625}+\sqrt{441}=25+21$ [ From ( 1 ) and ( 2 ) ]

$\therefore$ $\sqrt{625}+\sqrt{441}=46$