Square root

(5y-3)^2

(5y-3)^2

Square root

(5y-3)^2

(5y-3)^2

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

a^{2}-b^{2}=(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

a

Usually simplification requires removing squares from under the radical.

Examples

1/√2 = (1/√2)*((√2)/(√2)) = (√2)/(√2)

1/((√2)-√3) = (1/((√2)-√3))*((√2)+√3)/((√2)+√3) = ((√2)+√3)/((√2)

= ((√2)+√3)/(2-3) = -((√2)+√3)

√20 = √(4*5) = (√4)(√5) = 2√5

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