solve square root equations

Question

did I solve this correctly?

       _____        _____

     √5p + 5 = √6p + 1

 

      5p + 5 = 6p + 1

      5p + 5 - 5 = 6p + 1 - 5

      5p = 6p - 4

      5p - 6p = 6p - 6p -4

      -1p = -4    (divide by -1)

        p = 4

 

 

 

 

 

Answer 1

No that is not correct! You are close though!

if your equation is 

(√5)p + 5 = (√6)p + 1

up to this step:

(√5)p = (√6)p - 4

you are correct, but

(√5)p - (√6)p = - 4

does not become -p = -4.

using the distributive property:

(√5)p - (√6)p = - 4   =>   p( (√5) - (√6) ) = -4.

because it is a radical we cannot simplify (√5) - (√6) anymore and in fact, (√5) - (√6) = -0.21342176528...

so p = -4/((√5) - (√6))

 

if, however, your equation is:

√(5p) + 5 = √(6p) + 1

up to this step:
√(5p) = √(6p) - 4
you are correct, but
√(5p) - √(6p) = - 4

from here we need to take a different approach:

√(5p) - √(6p) = √5 x √p - √6 x √p.

using the distributive property we can pull √p to the side like so:

√5 x √p - √6 x √p = √p x (√5 - √6)

thus, 

√(5p) - √(6p) = - 4  =>  √p x (√5 - √6) = -4

=> √p = -4/(√5 - √6) => p = (-4/(√5 - √6))²

please look here for the radical and exponent rules:

 

http://www.shelovesmath.com/pre-algebra/exponents-roots-and-scientific-notation/