# How do you simplify sqrt( 8 x + 1) = 5?

Apr 9, 2016

$x = 3$

#### Explanation:

color(blue)(sqrt( 8 x + 1) = 5

Square both sides to get rid of the radical sign

$\rightarrow {\left(\sqrt{8 x + 1}\right)}^{2} = {5}^{2}$

$\rightarrow 8 x + 1 = 25$

$\rightarrow 8 x = 25 - 1$

$\rightarrow 8 x = 24$

color(green)(rArrx=24/8=3

Check

color(brown)(sqrt( 8(3) + 1) = 5

color(brown)(sqrt(24+1)=5

color(brown)(sqrt25=5

color(green)(5=5

Apr 9, 2016

$x = 3$

#### Explanation:

Square root is an 'action'. To 'get rid' of that action you reverse it!

The reverse of square root is to square it.

Square both sides giving:

${\left(\sqrt{8 x + 1}\right)}^{2} = {5}^{2}$

$\implies 8 x + 1 = 25$

Subtract 1 from both sides (the revers of add is subtract)

$8 x + 1 - 1 = 25 - 1$

$8 x = 24$

Divide both sides by 8 (the reverse of multiply is divide).

$\frac{8}{8} \times x = \frac{24}{8}$

But $\frac{8}{8} = 1$

$x = 3$