radical expression question.

Question

xochital · Answer

what is the product of $$3\sqrt{u}(\sqrt{448}+4\sqrt{7})$$

mathstudent55 · Answer

Distribute. Multiply the quantity outside the parentheses by each quantity inside the parentheses.

mathstudent55 · Answer

$ 3\sqrt{u}(\sqrt{448} + 4\sqrt{7}) $

$ = 3\sqrt{u}\sqrt{448} + 3\sqrt{u}(4\sqrt{7}) $

Can you simplify both terms?

xochital · Answer

so... $$3\sqrt{448u}+12\sqrt{7u}$$

mathstudent55 · Answer

Right. 
The right radical in simplified. The left one can be simplified further. What is the largest perfect square factor of 448?

mathstudent55 · Answer

The prime factors of 448 are:
$448 = 2^6 \times 7 $

xochital · Answer

21?

mathstudent55 · Answer

No.
2^6 is a factor of 448.
2^6 has an even exponent so it's the square of 2^3.
That means 2^6 is a perfect square.
2^6 = 64
448 = 64 * 7

xochital · Answer

oh okay

xochital · Answer

hmmm so what would this equation be simplified?

mathstudent55 · Answer

$3\sqrt{448u}+12\sqrt{7u} $

$= 3 \sqrt{64 \times 7u} + 12\sqrt{7u} $

mathstudent55 · Answer

$= 3 \sqrt{64} \sqrt{ 7u} + 12\sqrt{7u} $

$ = 3 \times 8 \sqrt{ 7u} + 12\sqrt{7u} $

$ = 24\sqrt{ 7u} + 12\sqrt{7u} $

$= 36\sqrt{7u} $

xochital · Answer

oh okay, thank you so much! :)

mathstudent55 · Answer

wlcm

mathstudent55 · Answer

Remember, the key to simplifying square roots is to factor out the largest perfect square factor. Since it's a perfect square, you can take its square root and remove the factor from the radical.