Question

celinegirl
PLEASE CHECK MY ANSWER - C

What is the product of Seven square root eight times four square root five? Simplify your answer.

A.) Twenty eight radical ten
B.) Fifty six radical two
C.) Fifty six radical ten
D.) Two hundred eighty radical four

Answer 1

\[(7\sqrt{8})(4\sqrt{5})\]
With the help of the radical identity \(\sqrt{a.b}=\sqrt{a}.\sqrt{b}\) we can separate, but first, let's convert the 7 and the 4 as radicals:
\[(\sqrt{49}\sqrt{8})(\sqrt{16}\sqrt{5})\]
And then, applying the identity I spoke about we get:
\[(\sqrt{49}\sqrt{8})(\sqrt{16}\sqrt{5}) \iff (\sqrt{(49)(8)})(\sqrt{(16)(5)})\]
But then again, we can re-apply the identity since we still have the product of two radicals:
\[(\sqrt{(49)(8)})(\sqrt{(16)(5)}) \iff \sqrt{(49)(8)(16)(5)}\]
Al you have to do now is operate those multiplications inside the radical and you'll get the answer.

Answer 2

@Owlcoffee you may have confused me a little bit ha. The answer I came up with is wrong?

Answer 3

It's quite simple, when you want to express a radical into it's mosr simple form, you first express everything in one radical and then using the identity you can simplify it further:
\[\sqrt{(49)(8)(16)(5)} \iff (7)(4)\sqrt{(8)(5)}\]

Answer 4

@Owlcoffee ohh okay

Answer 5

good job

Answer 6

\[280\sqrt{2}\]

Answer 7

??? @Owlcoffee

Answer 8

Show me your work

Answer 9

erm well thats the answer I got for \[(7) (4) \sqrt{(8) (5)}\]

Answer 10

is that wrong?

Answer 11

Show me how you operated the expression.

Answer 12

step by step.

Answer 13

is that necessary? I figured some out in my head and wrote some down..