Operations with Radical Expressions

Question

Determine whether √a+√a=2a is sometimes, always, or never true.  My Answer: never

 

A playground is shaped like a rectangle with a width 5 times its length, l. What is a simplified expression for the distance between opposite corners of the playground? My Answer: l √26

 

Solve the proportion.

 4/x=√11-1/3

 

 

 

Answer 1

1.  √a + √a = 2a

2√a = 2a

Divide both sides by 2:

√a = a

square both sides:

a = a²

0 = a²-a

0 = a(a-1)

 

a = 0 and 1     The expression is true for a = 0 and 1, but not for any other values of a.

 

2.  You got this one right (L√26). Good job.

 

3. I presume the proportion is actually:

4/x = (√11 - 1)/3

4*3/(√11-1) = x

12/(√11-1) = x

 

You now have to "rationalize" the denominator, which means get the radical out of the denominator.  We do this by multiplying the numerator and denominator by the conjugate of the denominator, √11 + 1:

 

12/(√11-1) * (√11+1)/(√11+1) = x

 

12*(√11+1)/(11-1) = x

 

6(√11+1)/5 = x