How do you find the square root of 35?

Answer 1

Square roots are not fun to figure out by hand, but you can do it.

First, let me explain what a square root is, just in case you're wondering.

sqrt(35) is asking, "What number times itself is 35?"

Now that that's sorted, you should see how square roots are the "opposite" of square numbers.

A square number is just the answer to "a number times itself"

Some easy perfect squares to remember are:

0 = 0x0

1 = 1x1

4 = 2x2

9 = 3x3

16 = 4x4

25 ... (you get the picture?)

36 ...

49 ...

64 ...

81 ...

100 = 10x10

121 = 11x11

144 = 12x12

169 = 13x13

Although, most people remember 0 squared through 10 squared.

So to find sqrt(35) let's look at our Perfect Square list (above)

What's the closest perfect square number that is smaller than (or equal to) our number 35?

Well, 36 is too big. and we know that's 6 x 6.

25 is smaller, so that works! and that's 5 x 5.

sqrt(35) is *just* smaller than 6, since sqrt(36) = 6.

and on the other hand, since 35 is bigger than 25, we know sqrt(35) is larger than 5.

sqrt(35) lies somewhere between 5 and 6, but very close to 6.

to get the exact amount, please use a calculator. :)

However, if you're asked to find the square root of one of the perfect squares, you shouldn't (read: don't) use a calculator. :) but, if you can't recall the perfect squares, it's OK.