#1
Simplify the expression: √12
3√2
ExplanationSquare root of 12 can be simplified to 3 times square root of 2.
#2
Rationalize the denominator: (1/√5)
(√5)/5
ExplanationTo rationalize the denominator, multiply numerator and denominator by the conjugate of the denominator.
#3
Simplify the expression: (√3 + √2)^2
5 + 2√6
ExplanationExpand the binomial square and simplify.
#4
Rationalize the denominator: (1/√10) + (3/√2)
(√10+3√2)/(20)
ExplanationRationalize each term separately using the conjugate.
#5
Simplify the expression: (√15 + √10)^2
25 + √150
ExplanationExpand the binomial square and simplify.
#6
Rationalize the denominator: (1/√13) + (4/√2)
(√13+4√2)/(26)
ExplanationRationalize each term separately using the conjugate.
#7
Simplify the expression: √18/√2
2√3
ExplanationDivide the numerator and denominator by √2 to simplify.
#8
Rationalize the denominator: (1/√7) + (2/√3)
(√21+2√3)/(21)
ExplanationRationalize each term separately using the conjugate.
#9
Simplify the expression: √48/√12
4√3
ExplanationDivide the numerator and denominator by √12 to simplify.
#10
Rationalize the denominator: (2/√6) + (5/√3)
(2√6+5√3)/(6)
ExplanationRationalize each term separately using the conjugate.
#11
Simplify the expression: √75/√3
5√3
ExplanationDivide the numerator and denominator by √3 to simplify.
#12
Rationalize the denominator: (3/√5) + (2/√3)
(3√5+2√3)/(5)
ExplanationRationalize each term separately using the conjugate.
#13
Simplify the expression: (2√10 + √5)^2
50 + 4√50 + 5
ExplanationExpand the binomial square and simplify.
#14
Simplify the expression: (3√7 - 2√5)^2
49 - 12√35 + 25
ExplanationExpand the binomial square and simplify.
#15
Simplify the expression: (4√11 - √7)^2
49 - 8√77 + 44
ExplanationExpand the binomial square and simplify.
#16
Simplify the expression: (√27 - √12)^2
9 - 4√108 + 12
ExplanationExpand the binomial square and simplify.
#17
Simplify the expression: (√32 - √18)^2
14 - 2√576 + 18
ExplanationExpand the binomial square and simplify.