very hard radical problems?

Question

Perform the indicated operation and simplify.

1.3sqrt(2) [3 + sqrt(2)]
2.4 + sqrt(20)/2
3. 12sqrt(18)/3sqrt(2)

please try to show work. thanks

Answer 1

1.)
3sqrt(2) * [3 + sqrt(2)]

Distribute for each term:

9sqrt(2) + 3sqrt(2)*sqrt(2) (Multiplying like roots cancels it out to the actual number, 2 in this case)
9sqrt(2) + 3*2
9sqrt(2) + 6

2.)
4 + sqrt(20)/2

Assuming that the 2 is being divided into ONLY the sqrt(20)...

4 + 2sqrt(5)/2 (The 2s cancel here because of division)
4 + sqrt(5)

In the case that the 2 is being divided into BOTH the 4 and the sqrt(2)...

[4 + 2sqrt(5)]/2
2 + sqrt(5)

3.)
12sqrt(18)/3sqrt(2)

Again, simplify the roots as much as possible...
12*3sqrt(2)/3sqrt(2) (The 3sqrt(2) cancels because of division)
12

So, your answers are
1.) 9sqrt(2) + 6
2.) 4 + sqrt(5) (or 2 + sqrt(5), depending)
3.) 12

Answer 2

Hey there!

Here are the answers.

1. 3sqrt(2)[3+sqrt(2)]--> Write the problem.
9sqrt(2)+3sqrt(2)sqrt(2)--> Use distributive property.
9sqrt(2)+3(2)--> Simplify sqrt(2)sqrt(2).
9sqrt(2)+6--> Simplify 3(2).
6+9sqrt(2)--> Use communitive property of addition.

2. 4+sqrt(20)/2--> Write the problem.
4+sqrt(5*4)/2--> Rewrite 20 as the product of 5 and 4.
4+sqrt(5)sqrt(4)/2--> Use the product of radicals property.
4+2sqrt(5)/2--> Simplify the above expression.
2+sqrt(5)--> Simplify the above expression.

3. 12sqrt(18)/3sqrt(2)--> Write the problem.
4[sqrt(18)/sqrt(2)]--> Simplify the quotient in the above expression.
4[sqrt(9*2)/sqrt(2)]--> Rewrite 18 as the product of 9 and 2.
4[sqrt(9)sqrt(2)/sqrt(2)]--> Use the product of radicals property.
4[sqrt(9)]--> Cancel out the sqrt(2).
4(3)--> Find the square root of 9, which is 3.
12 Multiply.

So, here are the answers to the problem.

1. 6+9sqrt(2)
2. 2+sqrt(5)
3. 12

Answer 3

1.3sqrt(2) [3 + sqrt(2)] =
(Distribute)
[3√(2)](3) + [3√(2)]√(2) =
9√(2) + 3(2) =
9√(2) + 6.

2.4 + sqrt(20)/2 =
4 + √(4*5) / 2 =
4 + 2√(5) / 2 =
4 + √(5).

3. 12sqrt(18)/3sqrt(2) =
(Simplify)
4√(9*2) / √(2) =
12√(2) / √(2) =
12.

Answer 4

Question 1
3√2.(3 + √2)
= 9.√2 + 3 x 2
= 9.√2 + 6
Question 2
4 + √20 / 2
= 4 + √(4 x 5) / 2
= 4 + 2√5/2
= 4 + √5
Question 3
12√18 / 3√2
= 12√(9 x 2) / (3 x √2)
= 36.√2 / 3.√2
= 12

Answer 5

1. 3sqrt(2)[3+sqrt(2)]=9sqrt(2)+3sqrt(2)sqrt(2)
=9sqrt(2)+6
2. 4+sqrt(20)/2=4+sqrt(4*5)/2=4+sqrt(5)
3.12sqrt(18)/3sqrt(2)=12sqrt(9*2)/3sqrt(2)=12

Answer 6

1. 8.6566406
2. 4+3.162277 =7.162277

3. 12*(4.2426) /3*1.41421=12

Answer 7

please try to do your own homework. thanks.