Question

How to take root without using calculator?

Answer 1

Suppose we have to find value of root225 then,

So,

$\sqrt{225} = 15.$

Hope this will help you. 

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Answer 2

Method 1 (with no dividing but it's slower)

Suppose you want the square root of 75.

As 82 = 64 and 92 = 81, you know the answer is somewhere between the two.

Try working out 8.52 and you get 72.25 (too small)

Now try 8.62 and you get 73.96 (too small but getting closer)

Now try 8.72 and you get 75.69 (too big)

Now you know the answer is between 8.6 and 8.7

Now try working out 8.652 and you get 74.8225 (too small)

Now try 8.662 ... and so on.

Keep going until you get an answer that's accurate enough for you.

If you want

the square root of a perfect square

Mrs Brooks bank (a maths teacher) told us to subtract the odd numbers in order 1,3,5,7 etc. until you get to zero then count up the number of subtractions!

Example . to get the square root of 36 it's:

36-1=35

35-3=32

32-5=27

27-7=20

20-9=11

11-11=0

Total number of subtractions = 6 therefore the square root of 36 = 6.

Method 2 (with nasty dividing but it's faster)

Again we'll try for the square root of 75.

As 82 = 64 and 92 = 81, you know the answer is somewhere between the two.

Guess it's 8.5 then work out 75/8.5 = 8.8235

Work out the average of 8.5 and 8.8235. It's (8.5 + 8.8235)/2 = 8.66175. This is a very close answer!

To get much closer, work out 75/8.66175 = 8.6588.

Work out the average of 8.66175 and 8.6588 to get 8.660275.

Hey - that's well close enough. 8.6602752=75.00036308. Now STOP SHOWING OFF.

Method 3 (using a formula)

KEITH FROM CANADA sent us this quick method which is usually accurate to about two decimal places. Here's his square root formula:

√X = √S + (X-S)/2√S

X = the number you want the square root of S = the closest square number you know to X

Let's try it on the square root of 75 again.

X=75 and so the nearest square number S = 81. This means that √S = 9.

Put the bits in the formula:

√75 = 9 + (75-81)/2*9

√75 = 9 + -6/18 = 9 - 0.333 = 8.667

Thanks Keith - we love it!

Short Cuts!

With some numbers you can make life easier for yourself and 75 is one of them.

Look and see if your number will divide by a square number. Here you'll see that 75 will divide by 25 and of course 25= 52. So you can put 75 = 25 x 3

If you work out the square roots you get sqrt(75) = sqrt(25) x sqrt(3).

sqrt (25)=5 and therefore sqrt(75)= 5 x sqrt3.

Of course you still need to know what sqrt(3) is, but the whole thing looks simpler now!