Question

Which expression is equivalent to sqrt10/4sqrt8

Answer 1

Answer:

Step-by-step explanation:

Since it's a division we need to look for a common factor to cancel

so first we try to break the numbers to there prime factors

$\frac{\sqrt{10} }{4\sqrt{8} } = \frac{\sqrt{2.5} }{4\sqrt{2.2.2} }$

So , now we try to factors that are common in top and bottom

$= \frac{\sqrt{2} \sqrt{5}}{4\sqrt{2}\sqrt{4} }$

common factor is sqrt 2 so lets cancel it

we get

$\frac{\sqrt{5} }{4\sqrt{4} }$

$\frac{\sqrt{5} }{8}$

Answer 2

We can break √10 into √2 • √5, and √8 into √2 • √4, or, simplifying √4 to 2, 2 • √2. Our expression now becomes

(√2 • √5) / (4 • 2 • √2)

Cancelling the √2 in the numerator and denominator gets us

√5/(4 • 2), or √5/8.