Simplifying Radicals Quiz

Study Notes

Simplifying Radicals

√60 can be simplified by finding the largest perfect square that divides 60 (which is 4), simplifying to 2√15.
√25x20y14 can be simplified by finding the square root of each factor, resulting in 5x2y7√5y.
√144x12y20 can be simplified by finding the square root of the perfect square factors, resulting in 12x6y10√y.
√121x2y22 can be simplified by finding the square root of the perfect square factors, resulting in 11x|y11|.
√81a36b8 can be simplified by finding the square root of the perfect square factors, resulting in 9a18b4.
√36x10y6 can be simplified by finding the square root of the perfect square factors, resulting in 6x5y3√x
√24 can be simplified by finding the largest perfect square that divides 24 (which is 4), simplifying to 2√6.
√8 can be simplified to 2√2.
√10/5 can be rationalized by multiplying the numerator and denominator by √5 resulting in √2/√5.
√27tu3 can be simplified by finding the largest perfect square that divides 27 (which is 9), simplifying to 3u√3tu.
√56m2n4p5 can be simplified by finding the largest perfect square that divides 56 (which is 4) and factoring out perfect squares from the variables, resulting in 2|m|n2p2√14p.
√9ab/√4ab4 can be simplified by finding the square root of both the numerator and denominator, resulting in 3/2b2√a.
8√30 - 4√30 can be simplified by subtracting the coefficients of the radicals, resulting in 4√30.
√27 + √18 + √300 can be simplified by finding the largest perfect square that divides each radicand and adding the coefficients of the like terms, resulting in 13√3.
(√2 + 2√8)(3√5 - √5) can be simplified by using foil method, simplifying each term and combining like terms resulting in 6√10 - 4√10.
√7 + √3 / √7 + √3 is a rationalization problem, multiply the numerator and denominator by the conjugate of the denominator which is (√7 -√3) resulting in 4/4 which simplifies to 1.