Square root
(5y-3)^2
(5y-3)^2
How Do I Simplify Square Root Algebra Problems?
Simplify 1 divided by 5 + square root of 2
Solve
x square root 2 minus 16 equals zero
x square root 2 minus 16 equals zero
2 divided by square root of 3
Different simplification problems require different approaches. Some square root problems are solved here and here and here.
For rational expressions with a square root in the denominator, you generally multiply by 1 renamed as the "conjugate" of the denominator divided by itself. This takes advantage of the factoring
a2-b2=(a+b)(a-b)
Usually simplification requires removing squares from under the radical.
Examples
1/√2 = (1/√2)*((√2)/(√2)) = (√2)/(√2)2 = (√2)/2
1/((√2)-√3) = (1/((√2)-√3))*((√2)+√3)/((√2)+√3) = ((√2)+√3)/((√2)2 - (√3)2)
= ((√2)+√3)/(2-3) = -((√2)+√3)
√20 = √(4*5) = (√4)(√5) = 2√5
For rational expressions with a square root in the denominator, you generally multiply by 1 renamed as the "conjugate" of the denominator divided by itself. This takes advantage of the factoring
a2-b2=(a+b)(a-b)
Usually simplification requires removing squares from under the radical.
Examples
1/√2 = (1/√2)*((√2)/(√2)) = (√2)/(√2)2 = (√2)/2
1/((√2)-√3) = (1/((√2)-√3))*((√2)+√3)/((√2)+√3) = ((√2)+√3)/((√2)2 - (√3)2)
= ((√2)+√3)/(2-3) = -((√2)+√3)
√20 = √(4*5) = (√4)(√5) = 2√5