How do you find the √ without a calculator PLEASE EXPLAI/SHOW WORK?

Question

Factor.
1) 784

2) 576

3)√ 675

4) PLEASE EXPLAIN. WHY CAN'T I TAKE 784/2 and /2???

5) Can I take √675 and divide 675/4=???

Answer 1

sqrt(675) = sqrt(25*27) = 5sqrt(9*3) = 15sqrt(3)
Factor out perfect squares than take out of square root ..

Answer 2

just factor starting simple til you get to a recognizable square

784 = 2 x 2 x 2 x 2 x 49 = 16 x 49 = 4^2 x 7^2 = 28^2
√784 = 28

576 = 2 x 2 x 144 = 4 x 144 = 2^2 x 12^2 = 24^2
√576 = 24

675 = 25 x 27 = 25 x 9 x 3 = 5^2 x 3^2 x 3 = 15^2 x 3
√675 = 15√3

Answer 3

Question 1
√784
√(2 x 392)
√(2 x 4 x 98)
√(2³ x 2 x 49)
√(2^(4) x 7²)
2² x 7
28

Question 2
√576
√(4 x 144)
√(4 x 12 x 12
√(4 x 4 x 3 x 4 x 3)
√4³ x 3
8 x 3
24

Question 3
√675
√(5 x 135)
√(5 x 5 x 27)
5 √3³
5 . 3^(3/2)

Hope this helps.

Answer 4

Find the numbers that go into these larger ones that can their square root is known and easy to calculate manually:

1. √ 784 = √ (49*16) = 7*4 = 28
2. √ 576 = √ (64*9) = 8*3 = 24
3. √ 675 = √ (25*27) = √ (25*9*3) = 5*3√ (3) = 15√ (3)
4. ?
5. √675 shouldn't be divided by 4 unless 4 is under the radical sign itself.

Answer 5

There is an ancient method for calculating square roots, and you can do it on paper with no calculator, but it will take you a while to do all the long division.

1. Start with your number, say 675.
2. Divide the number by your best guess for what the square root is (let's guess 25). 675/25 = 27.
3. Average the result with your previous guess to find your new guess: (25 + 27)/2 = 26
2. Divide the number by the new guess: 675/26 = 25.9615
3. Average the result with your previous guess to find your new guess: (26 + 25.9615)/2 = 25.9808
2. Divide the number by the new guess: 675/25.9808 = 25.9808

Voila, we've found the result, accurate to six digits. Each time you repeat this operation, you get twice as many digits of accuracy, so the number converges very fast.

Answer 6

u must put it into simplest radical form

so 784 = 49*16
√ 784=√ (49*16)=7*4=28

576=36*16
so
√ 576=√ (36*16)=6*4=24

675=25*27
so
√ 675=√ (25*27)=5√ 27
√27=√ 9*3
so
√ 675=5√ (9*3)=5*3√ 3=15√ 3

I don't understand your wording for number 4

And for number 5, it would be wiser to divide 675 by 25 like i did above...because 4 is not a perfect square and will make it more difficult to put it into simplest radical form.

Answer 7

The symbol √ means "square root". For 675, I would go like this:

20*20 = 400
30*30 = 900
So the square root is between 20 and 30; try 25

25*25 = 625
26*26 = 676
So 26 is *almost* right, the error is only +1.

A correction factor is:
New guess = old guess - error / (2*old guess)
New guess = 26 - 1/(52) = 26 - 0.01923
New guess = 25.98077
25.98077*25.98077 = 675.0004

The next correction is -0.0004 / 51.96154 = -0.0000079
This might be too small to bother with.

Answer 8

√x = x ^ (1/2)

Answer 9

1) 784
2 * 2 * 2 * 2 * 7 * 7

2) 576
2 * 2 * 2 * 2 * 2 * 2 * 3 * 3

3)
25.98^2

Answer 10

http://math.arizona.edu/~kerl/doc/square-root.html