Question

Find the value of √60025 and hence find the value of √600.25 + √6.0025.​

Answer 1

SOLUTION

TO DETERMINE

The value of √60025 and hence find the value of √600.25 + √6.0025.

EVALUATION

Here the given number is √60025

Now

$\sf{ \sqrt{60025} }$

$\sf{ = \sqrt{5 \times 5 \times 7 \times 7 \times 7 \times 7} }$

$\sf{ = 5 \times 7 \times 7 }$

$= 245$

Now

$\displaystyle\sf{ \sqrt{600.25} + \sqrt{6.0025} }$

$\displaystyle\sf{ = \sqrt{ \frac{60025}{100} } + \sqrt{ \frac{60025}{10000} } }$

$\displaystyle\sf{ = \frac{245}{10} + \frac{245}{100} }$

$= 24.5 + 2.45$

$\sf{ = 26.95}$

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Answer 2

Given : √60025

√600.25 + √6.0025

To Find :  value of √60025

and  value of √600.25 + √6.0025​

Solution:

          245

          60025

    2    4

       _____

          200

44       176

       _____

           2425

485     2425

       _______

             0

√60025 = 245

or

60025  = 5 * 5 * 7 * 7 * 7 * 7

=> 60025  = 5² * 7² * 7²

=>  60025  = (5 * 7 * 7 )²  

=>  60025  = (245)²  

=> √60025 = 245

√600.25 + √6.0025

= √60025/100   + √60025/10000

= √60025/ √100  +  √60025/ √10000

= 245/10  + 245/100

= 24.5 + 2.45

= 26.95

√600.25 + √6.0025  = 26.95

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