Math help: radicals/square roots...?

Question

uhg.. ok so i got my homework on the first day of school..math of coruse >.< and well... i forgot some stuff about square roots :\

i have this question..find the sqare root of 54..so far i have this

54

7 * 8

2* 4

2*2 so i have 7*2*2*2... how would i right this as an answer? and also.. sometimes one number is squared and one isnt in the answers..how do i know which one to put the square root sign over?

another question just says, 7 *3 (both squared). and it says simplify the expression, give the exact value in simplified form.

would it be 49 * 9? then i find the square root of that? (somehow) or what exactly?...help much appreciated :]

Answer 1

sqrt(54) doesn&#039;t equal 7*8

since 54=9*6, we can rewrite it as    sqrt(9*6),

which is the same as    sqrt(9)*sqrt(6)

since    sqrt(9)=3,

we can rewrite that as    3*sqrt(6)

so th final answer is:

3*sqrt(6)

unless by &quot;7*8&quot; you meant sqrt(56).

and since    56=4*14,

you can rewrite it as    sqrt(4)*sqrt(14)

since    sqrt(4)=2,

you can simplify it to    2*sqrt(14)

7^2 * 3^2 would equal 49*9,

since 49*9 = 441, your final answer would be 441

you dont need to take the sqare root of anything after that.

Answer 2

7*8 = 56 not 54 so lets try some other numbers

_/ = square root of what follows

_/56 = _/9*6 = _/9 * _/6

_/9 = 3

so _/56 = 3_/6

Answer 3

sqrt(56) =

sqrt(7*8) =

sqrt(7*2*4) =

sqrt(7*2)*sqrt(4) =

sqrt(14)*sqrt(2)*2 =

2*sqrt(14)

sqrt(54) =

sqrt(2*27) =

sqrt(2*3*9) =

sqrt(2*3)*sqrt(9) =

sqrt(2*3)*3 =

3*sqrt(2*3) =

3*sqrt(6)

If I am reading your second question correctly...

sqrt((7^2)*(3^2)) =

sqrt(7^2)*sqrt(3^2) =

7*3 =

21