1.Simplify (square root 7) (square root 14)? How do you do this?

Question

2. Simplify (2 square root 12) +(4 square root 27)?
I think I am getting thrown off because of the addition and multiplication, can anyone help?

Answer 1

1.
sqrt(7) sqrt(14)
= sqrt(7 * 14)
= sqrt(7 * 7 * 2)
= sqrt(7^2 * 2)
= sqrt(7^2) sqrt(2)
= 7 sqrt(2)

2.
(2 sqrt(12)) + (4 sqrt(27))
= (2 sqrt(4 * 3)) + (4 sqrt(9 * 3)
= (2 sqrt(4) sqrt(3)) + (4 sqrt(9) sqrt(3))
= (2 * 2 * sqrt(3)) + (4 * 3 * sqrt(3))
= 4 sqrt(3) + 12 sqrt(3)
= (4 + 12) sqrt(3)
= 16 sqrt(3)

Answer 2

1) √7 * √14 = √7 * √7*2 = √7 *√7*√2 =7 * √2
2) 2√12 + 4√27 = 2√3 * 4 + 4√3 * 9 = 2√3 * √4 + 4√3 * √9 = 4√3 + 12√3 = 16√3

Answer 3

1. Root 7 * Root 14

(a) Times 7 by 14:

= Root 98

(b) Now think of a square number which goes into 98...
The square number 49 goes in 2 times.

(c) So root 98 = root 49 * root 2

(d) Root 49 = 7, so the final answer is:

7 * root 2, which is written as 7 root 2

2. 2 root 12 + 4 root 27

(a) root 12 = root 3 * root 4
and root 27 = root 3 * root 9

(b) So root 12 = 2 root 3
and root 27 = 3 root 3

(c) So 2 root 12 = 4 root 3
and 4 root 27 = 12 root 3

(d) 4 root 3 + 12 root 3 = 16 root 3

Answer 4

Question 1
√7 √14 = √98 = √(49 x 2) = 7 √2

Question 2
2√12 + 4√27
2√(4 x 3) + 4√(9 x 3)
4√3 + 12√3
16√3

Answer 5

2 will factor out of first square root (with 3 staying from 12) and 3 factors out of the second square root (with one of the 3 from 27 staying) an you get:

4 square root 3 + 12 square root 3

Which is 16 square root 3

Answer 6

1. (square root 7) (square root 14) = (square root 7x14)
= (square root 98)

2. (2 square root 12) +(4 square root 27) = (4 square root 3) + (3 square root 3)
= (7 square root 3)

Answer 7

1. 7 square root 2

when multiplying square roots, all you need to do is multiply the numbers inside the square roots and stick a square root sign in front of it (7 times 14 = 98), the square root of 98 can be simplified to 7 square root 2, since 98 is equal to 49 times 2

2. 16 square root 3...


the 2 square root of 12 is equal to 2 times the square root of 3 times the square root of 4... which is simplified to 2 times 2 times the square root of 3, or 4 square roots of 3
the 4 square root of 27 is equal to 4 times the square root of 9 times the square root of 3... which is simplified to 4 times 3 times the square root of 3, or 12 square roots of 3

finally, just add 4 square root of 3 and 12 square root 3 to get 16 square root 3

Answer 8

1. When multiplying radicals, multiply inside the radicals and then simplify.

root7 (root14) = root(98)

root(98) = root(49 * 2) = 7root2

2. When adding radicals, the number inside the radicals have to be the same. To do this, therefore you need to simplify first.

(2root12) + (4root27)
2root(4 * 3) + 4root(9 * 3)
4root3 + 12root3

Now, once the number inside is equal, simply add the numbers outside.

16root3 is your answer.

Answer 9

factorize the number under square root and take the square terms out
example:
square root(12)=sqrt(2*2*3)=2sqrt (3)

Answer 10

1. 14=2*7 so SQRT(14) = SQRT(2*7) = SQRT(2)*SQRT(7)
this gives SQRT(7)*SQRT(2)*SQRT(7) = 7*SQRT(2)

2. 12 = 4*3 so 2*SQRT(12) = 2*SQRT(4*3) = 4*SQRT(3)
27 = 9*3 so 4*SQRT(27) = 4*SQRT(9*3) = 12*SQRT(3)
Add these together and get 16*SQRT(3)