Would someone please help me,?

√(ab) = √a*√b

For example, √8 = √(4*2) = √4*√2=2√2.

Also, for powers, taking the square root of a number an even power is alway the number raised to 1/2 of the original power (no square root):

√(aⁿ) =aⁿ/²) (if n is even)

(if n is odd, then the answer would be a(ⁿ-¹)/²*√a. This is easier to see with real examples:

√5¹² = 5^6

√5¹³ = (5^6)√5

So, showing your work:

√[81x¹²y^8z¹º] =

(√81)(√x¹²)(√y^8)(√z¹º) =

9(x^6)(y^4)(z^5)

2√[48] + 7√[12] –√[27]

Rationalize the denominator:

2____

√[3] + √[2]

to simplify, you just extract any whole square roots

similarly,

to rationalize the denominator, you multiply by the conjugate

if you use ^ as power