how do i get the answer to sqrt 14 sqrt 28 and the answer is 14 sqrt 2?

Question

square roots
when i feel that i have a technique then i try to use it on different problems i am running into problems.

Answer 1

sqrt(14) * sqrt(28)

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

Notice that I used two properties:

sqrt(a*b)=sqrt(a)*sqrt(b)
sqrt(a)*sqrt(a)=a

Answer 2

Well the technical way society teaches you is to multiply the numbers underneath the sqrt and then find a perfect square factor to factor and then carry out the math.

The easy way, especially for this problem, is to first factor the numbers:

sqrt(14) is alright for now, though...
sqrt(28) can be written as: sqrt(2*14)

Now 'multiply'

sqrt(14*14*2)

Since there is a 14^2 you can just simplify that to 14*sqrt(2) or 14sqrt2

Answer 3

√14 * √28
= √14 * √14*2
= √14 * √14 * √2
= 14√2

Answer 4

You have to multiply BOTH square roots and then reduce the square roots.

We have:

sqrt(14) times sqrt{28} = sqrt{392}.

sqrt{392} can be reduced.

sqrt{392} = sqrt{49} times sqrt{8}

The sqrt{49} is a perfect square because 7 times 7 = 49.

So, sqrt{49} = 7..We will use this 7 later.

The sqrt{8} = sqrt{4} times sqrt{2}

The sqrt{4} is another perfect square and so it becomes 2. We now multiply this 2 by the 7 we found above. See it?

Multiply 7 times 2 = 14.

What about the sqrt{2}?

Final answer:

14(sqrt{2})

Guido

Answer 5

Simplify: sqrt 14 sqrt 28
sqrt 2 * sqrt 7 * 2 * sqrt 7
sqrt 2 * 2 * 7 (because sqrt 7 * sqrt 7 = 7)
14 * sqrt 2

Answer 6

√14*√28=√14*28=√14*14*2=14√2

Answer 7

well, sqrt(14) * sqrt(28) = sqrt(14*28)
28 = 14*2, so we can rewrite as sqrt(14*14*2)
since 14 is repeated twice, we can take it out while leaving the 2 in the square root. therefore, we get:
14 * sqrt(2)

Answer 8

sqrt(14) * sqrt(28) = sqrt(14 * 28) = sqrt(14 * 14 * 2) = 14sqrt(2)

Answer 9

You have sqrt14sqrt28
sqrt28 is like sqrt(14*2)---------------------1
sqrt(14*2) can also be ---> sqrt14sqrt2--------------2
therefore sqrt14sqrt28 can be sqrt14sqrt14sqrt2---------3
and sqrt14sqrt14 is ==14
hence getting 14sqrt2 as in eqn. 2 above

Answer 10

√14*√28
√14*√14*2
(√14*√14)*√2
14√2