what is the ans of quesy
this
4√28+3√7+3√7
Answers
Step-by-step explanation:
This expression could be simplified in a few different orders, so ideas that differ from mine are not necessarily wrong. That said, I would start by rationalizing the denominator -- that is, multiplying both parts of the fraction by 7–√ since there's already a 7–√ there. This will force the denominator back into the integers, which is nice for various reasons.
428√37√=428√7√37√7√
=428√7√3∗7
=428√7√21
Now I happen to notice that 28 could be written as 4*7, which would be a convenient factored form to which to apply the property that the square root of a product is the product of its square roots. (For purposes of this property, "convenient factored form" is a factored form involving perfect squares to the greatest extent possible.)
=44∗7√7√21
=44√7√7√21
Then I use the fact that 4 is a perfect square to take its square root, and multiply the two \sqrt{7} factors together.
=4∗2∗721
I could multiply 4*2*7 at this point but I notice that I'll have to divide that 7 back out when I simplify the fraction, so instead...
=4∗2∗73∗7
=4∗2∗/73∗/7
=83
That's fully simplified but if this is an application problem I might restate the solution as 2\Frac23 or ≈2.67.
This last version also allows for checking my work. I know that 28−−√ is between 5 and 6 -- I'll guesstimate 5.2 since 28 is closer to 25 -- so the original numerator is around 20.8, and 7–√ is between 2 and 3 -- I'll guesstimate 2.5 -- so the original denominator is about 7.5. A pocket calculator tells me 20.8÷7.5=2.773, which looks close enough to attribute the difference to rounding error (but if you aren't comfortable with that difference, just get better estimates for the square roots).