Question

Change the expression to a single square root, or its opposite:

a) 2√2
b)-7√3
c)(1/3)√18b
d)5√y
e)-6√2a
f)−.1√200c

Answer 1

a)
`2√(2)=√(8)`

b)
`-7√(3) =-√(147)`

c)
`(1)/(3) √(18b) =√(2.b)`

d)
`5√(y) =√(25y)`

e)
`-6√(2a) =-√(72a)`

f)
`-0.1√(200c)=- \sqrt{2c`

Explanation:

a)
`2√(2)=( √(2) )^2.√(2)=(√(2))^3 = √(2^3) =√(8)`

b)
`-7√(3) =-(√(7) )^2√(3) =-√(7^2.3) =-√(147)`

c)
`(1)/(3) √(18b) =(1)/(3) √(9.2.b) =(1)/(3) √(3^2.2.b) =(1)/(3) * 3√(2.b) =√(2.b)`

d)
`5√(y) =√(5^2) √(y)=√(25y)`

e)
`-6√(2a) =-√(6^2)√(2a) = -√(36.2a) =-√(72a)`

f)
`-0.1√(200c)=-(1)/(10) √(10^2.2c) =-(1)/(10)*10 √(2c)=- \sqrt{2c`