Roots Always Become Smaller, Right?

Algebra Level 1

Which of the following mathematical symbol should we place in the box below to make the following statement true? 0.99 0.99 \large \sqrt{0.99} \; \Box \; 0.99

> > < < = =

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2 solutions

Hung Woei Neoh
May 18, 2016

For positive values x x with the range x > 1 x > 1 :

x < x \sqrt{x} < x

Eg. x = 4 , 4 = 2 , 2 < 4 x=4,\;\sqrt{4}=2,\;2<4

For positive values x x with the range 0 < x < 1 0 < x < 1 :

x > x \sqrt{x} > {x}

Eg. x = 0.01 , 0.01 = 0.1 , 0.1 > 0.01 x=0.01,\;\sqrt{0.01} = 0.1,\; 0.1 > 0.01

0.99 0.99 falls into the second category, therefore 0.99 > 0.99 \sqrt{0.99}\; \boxed{>} \,0.99

Perfect, beautiful solution +1 :-)

akash patalwanshi - 5 years ago

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Thanks ¨ \ddot \smile

Hung Woei Neoh - 5 years ago

Awesome! (+ 10 {10}^{\infty} )

Ashish Menon - 5 years ago

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Thanks ¨ \ddot\smile

Hung Woei Neoh - 5 years ago

Wounderful

Patience Patience - 2 years, 8 months ago
Amed Lolo
May 25, 2016

√.99=.99^.5 so. Ln√.99=.5Ln.99. Ln.99=-ve value so ln√.99>ln.99 ln is increasing function so √.99>.99#######

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