Question

square root of 625 + square root of 441 is​

Answer 1

Given: $\sqrt{625}+\sqrt{441}$

Square of 25 and 21 is,

$25^2=625\\21^2=441$

$\sqrt{625}+\sqrt{441}=25+21$

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

Answer 2

square root of 625 + square root of 441 is 46

Given :

The numbers 625 , 441

To find :

The square root of 625 + square root of 441

Solution :

Step 1 of 3 :

Find square root of 625

We first prime factorise the number 625

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{5}}}&{\underline{\sf{\:\:625 \:\:}}}\\ {\underline{\sf{5}}}&\underline{\sf{\:\:125 \:\:}} \\ {\underline{\sf{5}}}&\underline{\sf{\:\:25 \:\:}} \\\underline{\sf{5}}&\underline{\sf{\:5\:\:}}\\\underline{\sf{}}&\underline{\sf{\:\: \: 1\:\:} }{\sf{\:\: \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

625 = 5 × 5 × 5 × 5

Thus we get

Square root of 625

$\displaystyle \sf{ = \sqrt{625} }$

$\displaystyle \sf{ = \sqrt{5 \times 5 \times 5 \times 5} }$

$\displaystyle \sf{ = \sqrt{ {5}^{2} \times {5}^{2} } }$

= 5 × 5

= 25

Step 2 of 3 :

Find square root of 441

We first prime factorise the number 441

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:441 \:\:}}}\\ {\underline{\sf{3}}}&\underline{\sf{\:\:147 \:\:}} \\ {\underline{\sf{7}}}&\underline{\sf{\:\:49 \:\:}} \\\underline{\sf{7}}&\underline{\sf{\:7\:\:}}\\\underline{\sf{}}&\underline{\sf{\:\: \: 1\:\:} }{\sf{\:\: \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

441 = 3 × 3 × 7 × 7

Thus we get

Square root of 441

$\displaystyle \sf{ = \sqrt{441} }$

$\displaystyle \sf{ = \sqrt{3 \times 3 \times 7 \times 7} }$

$\displaystyle \sf{ = \sqrt{ {3}^{2} \times {7}^{2} } }$

= 3 × 7

= 21

Step 3 of 3 :

Find square root of 625 + square root of 441

Square root of 625 + Square root of 441

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

$\displaystyle \sf{ = 25 + 21 }$

$\displaystyle \sf{ = 46 }$

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