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Maths - Square Root

by Ross
(Lucknow, UP, India)











































1-10underroot5000/105000*100

compute the value of the given statement in two different ways:

1. Compute the decimal value

2. Simplify the mathematical expression to the maximum extent possible, without converting the expression to its decimal equivalent.

Comments for Maths - Square Root

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Sep 14, 2011
Evaluate Expression - Square Root
by: Staff


The question:

by Ross
(Lucknow, UP, India)


1-10underroot5000/105000*100


The answer:

1-10underroot5000/105000*100

= 1 - 10√[(5000/10500)*100]

= 1 - 10√[(5000*100)/10500]

= 1 - 10√[(500000)/10500]

= 1 - 10√[(5000)/105]

= 1 - 10√(1000/21)

≈ 1 - 10√(47.6190476190476)

≈ 1 - 10*6.9006555934235

≈ 1 - 69.006555934235

≈ - 68.006555934235


OR


= 1 - 10√[(5000/10500)*100]

= 1 - 10*√[(5000*100)/10500]

= 1 - 10*√[(500000)/10500]

= 1 - 10*√[(5000)/105]

= 1 - 10*√(1000/21)

= 1 - 10*√(1000) / √(21)

= 1 - 10*[√(1000) / √(21)]* [√(21) / √(21)]

= 1 - 10*{[√(1000)] * [√(21)] } / {[√(21)] * [√(21)]}

= 1 - 10*{[√(1000)] * [√(21)] } / 21

= 1 - 10*[√(1000*21)] / 21

= 1 - 10*[√(21000)] / 21

= 1 - 10*[√(100*210)] / 21

= 1 - 10*[√(10²*210)] / 21

= 1 - 10*[√(10²)*√(210)] / 21

= 1 - 10*[10*√(210)] / 21

= 1 - [10*10√(210)] / 21

= 1 - [100√(210)] / 21



The final answer is:

≈ - 68.006555934235

or

= 1 - [100√(210)] / 21



Thanks for writing.

Staff
www.solving-math-problems.com



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