Question

what is the product of sqrt t (6 - 2 sqrt 7)?

A) 6 sqrt t - 2 sqrt 7
B) 6 sqrt t - 2 sqrt 7t
C) 4t sqrt 7
D) 4 sqrt 7t

Answer 1

\(\sqrt{t}(6-2\sqrt{7})\) is just like a(b-c).

You can use the distributive property: a(b-c)=ab-ac.

Answer 2

Also, use this rule for roots: \(\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}\)

Answer 3

but how would I use that with the equation? I don't understand :/

Answer 4

OK, let's see what to do:
\[\sqrt{t}(6-2\sqrt{7})=\sqrt{t} \cdot 6 - \sqrt{t}\cdot 2\sqrt{7}\]
I used the distributive property (distributed √t between the two numbers in brackets).

Answer 5

Tidy up a bit: \(6\sqrt{t}-2\sqrt{t}\sqrt{7}=6\sqrt{t}-2\sqrt{7t}\)
Now I used the rule I mentioned about roots.

Answer 6

Oh, okay
Thank you @ZeHanz