Square of roots

Algebra Level 1

Evaluate $\sqrt{3^2} + \sqrt{4^2} + \sqrt{ 3^2 + 4^2 }$ .

7 solutions

Andhika Rahardian
Oct 23, 2013

The question is $\sqrt{3^{2}} + \sqrt{4^{2}} + \sqrt{3^{2}+4^{2}}$

$\sqrt{3^{2}}=3$ , $\sqrt{4^{2}}=4$ and $\sqrt{3^{2}+4^{2}}=5$

BUT $\sqrt{3^{2}+4^{2}}$ $\neq$ 7 because we must add first the numbers in that root

so , the answer is $3+4+5 = \boxed{12}$

Can you explain why $\sqrt{3^2+4^2} = 5$ ?

Calvin Lin Staff - 7 years, 7 months ago

$3^{2}$ = 9 and $4^{2}$ = 16 ; 9+16 = 25 its root is 5 , as 5*5=25

Piyush Ranjan - 7 years, 7 months ago

$3^{2}=9$ and $4^{2}=16$

so $\sqrt{{3^{2}}+{4^{2}}}$ $=$ $\sqrt{9+16}$ = $\sqrt{25}$ $=$ $\boxed{5}$

Andhika Rahardian - 7 years, 7 months ago

Sayan Mandal - 7 years, 7 months ago

but root of (3+4)^2=3+4=7?? Explain this

Ahmad Adnin - 7 years, 7 months ago

$3^{2}$ = 9 and $4^{2}$ = 16 ; 9+16 = 25 its root is 5 , as 5*5=25

Piyush Ranjan - 7 years, 7 months ago

It is a common mistake to think that $\sqrt{a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2} = a + b$ .

This question catches those who made such a mistake, and guides them towards correcting it.

Calvin Lin Staff - 7 years, 7 months ago

James Holcombe
Oct 21, 2013

The problem is equal to 3 + 4 + 5 = 12

R J
Oct 20, 2013

$\sqrt{3^2}$ =3 $\sqrt{4^2}$ =4 $\sqrt{3^2 + 4^2}$ =5 * ANSWER IS * = * 3+4+5 = 12 *

Piyush Ranjan
Oct 25, 2013

exp = 3 + 4 + root (9+16) = 3+4+5 =12. :)

Noel Quirol
Oct 20, 2013

Its is just equal to 3+4+sqrt.of 25 = 3+4+5 = 12 ..

Patrick Feltes
Mar 28, 2014

3 + 4 + 5 = 12

Nimesh Patodi
Dec 30, 2013

3+4+5=12