Question about simplifying square roots..?

Question

Okay so I have to find the square root of 5376.
If you absolutely CAN'T find that one what would 1344's be.
And it can't be a decimal it has to simplified. Like 2 then a square root symbol and then 5 (for example)

I'll just say it again, because the first answer isn't what I was asking for, I was wondering what is was SIMPLIFIED, as in NOT A DECIMAL

Answer 1

Ok, first you find the largest square that goes into it...

sqrrt5376 {4 goes into 5376}

2sqr1344 {4 goes into 1344}

4sqt336 {4 goes into 336}

8sqt84 {4 goes into 84}

16sqt21 {and that's the end}

I'm sure there should be a shorter way, but hey, at least I did it for you! :P

Answer 2

√5376 = √2^6 X 84 = 8√42 (simplest form, without decimals)

I also found out that 1344 is a multiple of 5376, so 1344 simplified would be 4√42

So final answer would be indeed 16√21 for 5376 and 4√42 for 1344...

Answer 3

It is going to be pretty difficult to simplify a number that is not a perfect square. You could simplify by making 5376 into (84X64). Then the answer would be 8 times the square root of 84.

Answer 4

First you need the prime factorization of 5376.

I can divide the number 5376 by the first prime number, 2, eight times. The remainder is 21, which only has two factors, 3 and 7 -- each of which is prime.

so
sqrt(5376) =
sqrt(2*2*2*2*2*2*2*2*3*7)=

Now for every pair of the same factor, one comes outside the radical. Thus,
= 2*2*2*2 sqrt(3*7)
= 16sqrt(21)

Answer 5

5376 = 256 * 21 = (2^8) * 21
Take sqrt of both sides:
Sqrt 5376 = (2^4) * (sqrt 21) = 16 * (sqrt 21)

1344 = 64 * 21 = (2^6) * 21
Sqrt 1344 = (2*3) * (sqrt 21) = 8 * (sqrt 21)

Voila!

Answer 6

sqr(5376) = 73.3212
sqr(1344) = 36.66

long process . . .
group the number into two digit from the decimal point
53'76'
nearest square root of 53 is 7
7x 7 = 49 . . . subtract this to 53
53 - 49 = 4 . . . . bring down or join the 76 . . next group
4 . . 76 . . => . . 476
partial divisor is 7 x 20 = 140
476 / 140 = 3. . .. place this in the answer . . . it is now 7 & 3 or 73
143 x 3 = 429 . . . . . . . . subtract 476 - 429
476 - 429 = 47 . . . . bring down two zeroes . . .. 00
47 . . 00 . . => . . 4700 . . . . this is the new divident
partial divisor is 73 x 20 = 1460
4700 / 1460 = 3 . . . . place this to the answer . . . 73.3
... .. . etc . . . repeat the process

Answer 7

sqrt(5376)
=sqrt(16*336)
=sqrt(64*84)
=8*sqrt(84).ANS or 16* sqrt(21).
or using calculator:73.32. ANS

Answer 8

5376=256*21
So sqrt(5376) = sqrt(256)*sqrt(21) = 16sqrt(21)

Answer 9

16sqrt21 this is the same as sqrt 256*21. sqrt256*sqrt21=16sqrt21

Answer 10

rt5376=rt(4)rt(1344)
=rt(4)rt(4)rt(336)
=rt(4)rt(4)rt(4)rt(84)
=rt(4)rt(4)rt(4)rt(4)rt(21)
=2 x 2 x 2 x 2 rt21
=16rt21