help with these math problems dealing with radicals?

Question

simplify each expression:
1) √180
2) 3√18

combine the radicals:
1) √18 + √8 - √32
2) 3√20 - 2√45

multiply or divide then simply:
1) 8√2 x 2√2
2) (3√5)^2
3) (16√21) / (2√7)
4) (5√162) / 9√50

the expression √108 - √3 is equilvalent to:
1) √105
2) 35√3
3) 5√3
4)6

the sum of 9√2 and √32 is:
1) 9√34
2) 13√2
3) 10√34
4) 15

Answer 1

Simplify each expression:
1) sqrt 180 = sqrt (36*5); 36 is a perfect square.
= 6 sqrt 5
2) 3 sqrt 18 = 3 sqrt (9*2); 9 is a perfect square.
= 9 sqrt 2
Combine the radicals:
1) sqrt 18 + sqrt 8 - sqrt 32 = 3 sqrt 2 + 2 sqrt 2 - 4 sqrt 2
= sqrt 2
2)3 sqrt 20 - 2 sqrt 45 = 3 sqrt (4*5) - 2 sqrt (9*5)
= 6 sqrt 5 - 6 sqrt 5
= 0

Multiply or divide then simplify:
1) 8*2*((sqrt2)^2)) = 16 * 2 // sqrt 2 raised to 2 is equal to 2.//
= 32
2) (3 sqrt 5)^2 = 9 * 5 //sqrt 5 raised to 2 is equal to 5.//
= 45
3) (16 sqrt 21)/(2sqrt7) = (16 sqrt 3 sqrt 7) / 2 sqrt 7
= 8 sqrt 3
4) (5 sqrt 162)/(9 sqrt 50) = ( 5 sqrt (81*2))/(9 sqrt (25*2))
= (45 sqrt 2)/(45 sqrt 2)
= 1

The expression sqrt 108 - sqrt 3 is equal to (sqrt (36 * 3)) - sqrt 3. Thus, the expression is equal to 5 sqrt 3.

The sum of 9 sqrt 2 and sqrt 32 is equal to (9 sqrt 2 + sqrt (16*2)). Hence, the sum is 13 sqrt 2.

Answer 2

combine the radicals:
1) √180 = √(5*36) = 6√5
2) 3√18 = 3√(2*9) = 9√2

combine the radicals:
1) √18 + √8 - √32 = 3√2 + 2√2 - 4√2 = √2
2) 3√20 - 2√45 = 6√5 - 6√5 = 0

multiply or divide then simply:
1) 8√2 x 2√2 = 32
2) (3√5)^2 = 45
3) (16√21) / (2√7) = 8√3
4) (5√162) / 9√50 = (45√2)/(45√2) = 1

the expression √108 - √3 is equilvalent to:
3) 5√3

the sum of 9√2 and √32 is:
2) 13√2

Answer 3

1) √9 √20
√9 √4 √5
3*2 √5
6√5
2) 3√2 √9
3 √2 *3
9√2

1) √9√2 + √4√2 - √16√2
3√2 + 2√2 - 4√2
√2
2) 3√4√5 -2√9√5
3*2√5 - 2*3√5
6√5 -6√5
0

1) 16√2
2) 9*5=45
3) (16√7√3)/(2√7)= 8√3
4) 5√81√2 / 9√25√2= 45√2 / 45√2 =1

3) 5√3

2) 13√2

Answer 4

For example:
2) 3√18

the √18 and split into √9 * √2
=√9=3 * √2 (3)
=9√2

Answer 5

sqrt of 180=sqrt of 36*sqrt of 5= 6 sqrt of 5
3 sqrt of 18= 3 sqrt of 9* sqrt of 2= 9 sqrt of 2
sqrt of 18 +sqrt of 8- sqrt of 32= 3 sqrt of 2+ 2 sqrt of 2
- 4 sqrtof 2= sqrt of 2
3 sqrt of 20- 2 sqrtof 45= 3( sqrt of 4 * sqrt of 5)-(sqrt of 9*
sqrtof 5)= 6 sqrt of5- 3 sqrt of 5= 3 sqrt of 5
8 sqrt of 2* 2sqrt of 2=16 sqrt of 2
(3 sqrt of5)^2= 45
5sqrt of 162 / 9 sqrt of 50= 45 sqrt of 2 / 5 sqrt of 2=9sqrt of 2
sqrt of 108-sqrt of 3=6 sqrt of 3-sqrt of 3= 5 sqrt of 3
9 sqrt of 2 + sqrt of 32 = 9 sqrt of 2 +4 sqrt of 2=13 sqrt of 2
16 sqrt of 21 / 2 sqrt of 7= 16 sqrt of 7 * sqrt of 3 / 2sqrt of 7=
8 sqrt of 3*