Solving Square Root Problems: 10^2+10^2 to 10*√(2)

[christian0710]

Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)?

Kind regards,
Christian

 

[pwsnafu]

Well, what do you get when you add a number to itself?

 

[Mentallic]

Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)?

Kind regards,
Christian

These rules apply:

$$\sqrt{ab}=\sqrt{a}\sqrt{b}$$

$$ab+ac=a(b+c)$$

 

[christian0710]

Ohh of course! thank you very much :)
So it's

sqrt(10^2 +10^2) = sqrt(2*10^2) = sqrt(10^2)*sqrt(2)= 10*sqrt(2).

 

[Deepak suwalka]

$\sqrt{10^2+10^2}$

$\sqrt{a^2+a^2}=\sqrt{2a^2}$

Similarly

$\sqrt{10^2+10^2}=\sqrt{2(10)^2}$

$\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$

Similarly
$=\sqrt{2(10)^2}=\sqrt{2}\cdot\sqrt{10^2}$

$=10\sqrt{2}$